At the same time they dented the championship hopes of in-form Marton, who lost their 11-match unbeaten record and the chance to share the league leadership.
Fellow strugglers, Northallerton and Middlesbrough, who have been dragged closer to the danger zone, were among those teams unable to play, so the fact
that Bishops managed to make a delayed start became a massive incentive they couldn't afford to waste.
With Dan Conway getting two early wickets for the hosts, Marton found batting conditions difficult and had to fight hard after slumping to 72-5.
John Glendenen, who top-scored with 39, produced a wealth of good shots to keep Marton in the game but the 148-9 with which they finished in their reduced 37 overs never looked quite enough.
Certainly Bishops' bowling trio of Conway (3-36), Phil Holdsworth (2-20) and Richard Hawthorne (2-53) had been happy to exploit the better of the conditions.
With the pitch getting easier, Bishops didn't need to take any risks as Matthew Cowling (32) and Ryan Nicholson (30) got them off to a steady start. Craig George hit 31 before skipper Holdsworth
(29no) and Hawthorne (21no) added the final partnership worth 37 runs to take the victory.
They needed 21 to win from the last three overs, including five from the final six balls, and, in the gloom, got the winner from the last delivery.
Marton's disappointment could not have been greater because, had they won, they would have gone level on points with leaders Hartlepool, whose match at
Northallerton never got started because of heavy rain.
Marske might have hoped their game with Darlington had suffered a similar fate but despite a damp outfield it went ahead on time and without any
The Seasiders, however, suffered a 12th defeat which dropped them to the foot of the table.
The Quakers made a challenging 182-4, with 79 from Rajin Saleh and 51 from Jack Vickerman, before the league's top wicket-takers, Peter Armstrong (4-24) and Doug Mulholland (4-52), who have 106
wickets between them, bowled out Marske for just 129 to register victory by 53 runs.
Barnard Castle won with just four balls of the match remaining at Great Ayton, where Gary Pratt hit 64 to take him to 832 in the league for the season
and make him the leading run-maker.
Josh Thompson (68) and Jon Grainge (53) enjoyed an 83-run partnership as Ayton totalled 166-6, but Barney won by seven wickets and moved into fourth place in the table after Ben Usher (60no)
smashed six sixes, including one to win the game, in a 55-ball onslaught.
Waterlogged outfields caused early postponements of the games at Normanby Hall v Guisborough and Stokesley v
Middlesbrough, but it was a cloudburst at Richmond 12 overs into the match with Billingham which led to its
abandonment, with the Synners on 50-2.
Today, Bishop Auckland continue their battle for survival with a game at Park Drive against leaders Hartlepool, while Marske entertain Barnard Castle and Northallerton travel to Billingham. Marton
seek to get over Saturday's disappointment with a match at Fountains Garth, where they play Guisborough.