Atkinson, signed as a replacement for Mark Bell, pushed an Andy Johnson spot-kick against the post to keep alive West’s slim hopes of catching the top two.
Manager Peter Dixon was unhappy with a yellow card given to striker Stuart Banks for simulation in the Bishops’ box when he appeared to be on the receiving end of a reckless tackle.
But he was delighted with the result, saying: “Since I took over three years ago, we’ve never lost to Bishop Auckland.
“The lads on the bench teased Neal as he was preparing to face the penalty, asking quite loudly if he was enjoying his debut! Again, the players showed plenty of character to come back from two down.”
Bishops took the lead after six minutes when Kieran Megran found space in the area to slot the ball past Atkinson, and after Andy Johnson smashed a shot against the bar, former West player Dale Jardine won the ball inside the area and chipped the keeper for the second.
But West hit back with three before the break.
Richard Paxton swept home from six yards from a freekick, then Mattie Moffat dispossessed a defender and nutmegged Peter Jeffries for his 15th league goal of the season.
Trickery by John Campbell on the right helped him cross for Banks to head in from six yards.
They got a fourth at the start of the second period when Elliott Gardner turned in a low Campbell cross at the near post, and they missed two more easy chances.
Johnson pulled one back from the edge of the area, and in the last minute he was tripped in the box for the penalty award. But Atkinson dived low to his left to save.
Bishops’ manager Colin Myers said: “I don’t think we deserved to get anything out of the game because our defending was very poor at times.
“We gifted them three goals.
We’ve still got a chance of finishing third, but it’s usually about this time of year when Whitley Bay come good. They might even catch the top two.”
Champions Spennymoor Town were held to a goalless draw at home by Bedlington to slip nine points behind Darlington, but they still have five games in hand and are unbeaten in 22 league games.
Moors hit the woodwork through Wayne Phillips and Joe Walton. They rallied near the end, and Gavin Cogdon had a 20-yarder tipped over the bar by Jack Norton, while Micky Rae put a glancing header just wide.
Despite dropping two points, Moors have kept 15 clean sheets this season.
Newton Aycliffe climbed further away from the bottom two with an 3-1 win at Consett.
After a good shot by Fred Woodhouse took a deflection and beat Consett keeper Chris Elliott, Aycliffe keeper Scott Pocklington kept his side in the lead by making an excellent save. Luke Sullivan put a penalty off target for Consett before they equalised with an effort from the edge of the box by Andy Cuthbertson.
Aycliffe regained the lead when Shaun Reay held the ball up and set up Woodhouse to score from six yards, then former Darlington player Reay scored his first goal for Aycliffe with a shot on the turn into the bottom corner.
Durham City’s recent good run came to an end when they lost 3-2 at fourth-bottom Penrith.
Martyn Coleman put Penrith into the lead after 43 minutes and scored the second just after half-time through Stephen Rigg. The game was held up for ten minutes because of an injury to the referee, and he had to be replaced by one of his assistants, while a spectator volunteered to run the line.
Scott Allison made it 3-0 to Penrith, before Durham staged a late rally with two goals by Scott Fenwick.
Billingham Town pulled Newcastle Benfield closer to the relegation zone by beating them 2-1 at Bedford Terrace.
They took the lead after nine minutes when Nicky Martin scored from a Harrison Davies pass, and they missed further chances. Benfield’s Ian Graham levelled after the break with a firsttime shot but Town scored the winner after 77 minutes when Josh McDonald crossed for Martin, under pressure from a defender, to score his 12th league goal of the season.
Teams with Vase ties on Saturday week, Ashington and Dunston, drew 1-1 at Woodhorn Lane.
After plenty of chances in the first-half, Ashington took the lead on 56 minutes when a shot by Andy Dugdale fell for Greg Bainbridge to beat Luke Connell in the Dunston goal.
However, Dunston stretched their unbeaten run to 14 matches when Steve Preen scored from a cross by Lee McAndrew.
Ashington assistant manager Perry Briggs made the trip to the West Country to watch Vase opponents Bodmin, but the game was postponed when he got there.
Hebburn reinforced their position in the top eight with a 4-0 home win over Billingham Synthonia. Tony Stephenson gave them the lead from a Lee Harrison cross after ten minutes, then Scott Robson got the second with a 25-yarder. Stephen Forster scored the third with a deep cross that deceived keeper James Montgomery, then he set up Stuart Nicholson to grab the fourth.
Sunderland RCA drew 3-3 with Guisborough after leading 2-0 thanks to two goals by Gary Shaw in the first 20 minutes, but Guisborough pulled a goal back when Mikey Roberts was fouled in the area and Jamie Poole scored from the spot.
Lewis Wood equalised with a deflected shot, then a cross by Gary Wood went through a crowd of players and ended up in the net. RCA levelled through Aristote Guerin- Lokonga, who dribbled through and fired past keeper Danny Dixon.
Celtic Nation and Team Northumbria also shared six goals in a 3-3 draw.
CN went 2-0 up through Graeme Lee and a John Sherlock own goal, but Peter Watling pulled a goal back.
CN went 3-1 up through a Michael Reed header, but Watling and Mark Fenwick hit back for TN.
In the second division, leaders Crook Town came from behind to pick up three valuable points at fellow promotion challengers Jarrow Roofing.
Roofing took the lead when former Crook striker Andy Appleby pounced on a rebound, but Crook full back Dave Gordon equalised with a cross-cum-shot from the left.
Liam McBryde restored Roofing’s lead with a header, but Crook replied again when Warren Byrne’s shot from the edge of the box was deflected in off Kyle Davis.
Roofing had a strong penalty claim turned down, before Robbie Bird fired the winner for Crook into the bottom corner.
Darren Atkinson, the new permanent manager of second bottom Horden, saw his side lose 5-0 at promotionchasing Ryhope CW, for whom Chris Winn scored his third hat-trick of the season.
He got the first two before half-time, and after the break, Michael Charlton and Jonny Butler got two more before Winn completed his haul.
Winn has 30 league goals for the season, while Butler has scored 34.
Seaham Red Star stayed well in touch with the leaders, winning 2-1 at Whickham.
Channon North put them into an early lead , with Kris Goss making it two. Andrew Snaith pulled a goal back for the home side.
Tow Law finally recorded their first home win of the season, defeating Esh Winning 3-0.
Mattie Scott gave them a great start in the opening minutes, and he scored his 13th league goal of the season soon after the restart. It was all over when Esh defender Craig Garthwaite scored an own goal.
The result of the day was lowly Brandon’s 2-1 home win over promotion-chasing Northallerton, who suffered only their second away league defeat.
Carl Chillingsworth put Northallerton into the lead on 49 minutes, but Glen Hendrix and Andrew Blackburn hit back for the home side to record only their fifth win.
Darlington RA suffered a 9- 1 thumping at Morpeth, for whom Micky Chilton became the fourth player to score five in a league game this season, with Steven Anderson (2), Eddie and Jordan Fry getting the others.
Jim Muir replied from the spot for the RA in the first half, but they trailed 6-1.
North Shields were also among the goals, scoring six without reply at Thornaby.
Rob Nolan (2), Dean Holmes and Keith Douglas were on the mark before sub Kieran Wrightson scored two more.
Birtley won for the first time in 16 games, their 2-0 victory at Ryton and Crawcrook giving them a seven-point breathing space over the bottom two.
Goalkeeper Andy Hunter saved a Paul King penalty, and Birtley took the lead when Scott Wallace scored from a corner. They got their second when defender Callum Turnbull put a corner into his own goal.
Chester-le-Street beat Whitehaven 2-1. Michael Pattison scored the first goal from a rebound off the keeper, but the Cumbrians levelled with a Sam Smith penalty following a foul by Shaun Smith.
Chester got the winner when Whitehaven defender Dave Lewis turned a Pattison cross into his own net.
The league has revealed that Willington and Heaton Stannington, have applied for membership next season, but they will need to finish in a promotion position and have a ground up to standard.
In the Evo-Stik League, Whitby had a 5-2 win at Marine to put them five points above the relegation zone.
Graeme Armstrong (2), Craig Farrell (2) and Stephen Snaith got the goals.
Blyth defeated Matlock 2-1 at Croft Park through Wayne Buchanan and an own goal.