After losing 5-0 at Preston in midweek, Pools couldn't afford a second successive reverse.
And they avoided it thanks to Monkhouse's late volley.
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Two goals from striker Marvin Morgan looked like securing Shrewsbury a first away win back in League One, before the substitute struck crisply home with time running out.
Pools took the lead on 15 minutes. Evan Horwood's crossfield ball picked out Steve Howard and his header was directed for Jon Franks to confidently volley in.
Home keeper Scott Flinders had to make an epic save to deny Matt Richards a quick leveller, but he was soon beaten.
After Pools’ defender Sam Collins had a shot blocked on the line, a long free-kick from Joe Jacobson fell kindly for Morgan to net from 12 yards.
Then, with seven minutes to go, the Shrews scored.
Pools should have been celebrating a goal - Franks passed up the chance to shoot from an inviting position and instead wasted the chance to pick out Howard or Monkhouse in the area.
The Shrews cleared on the counter-attack and Morgan got away to finish on 83 minutes.
Monkhouse levelled, but even then there was drama as Flinders had to be alert to save from Morgan and deny the striker a hat-trick.
HARTLEPOOL UNITED: Flinders; Baldwin, Collins, Hartley, Horwood; Lynch (Monkhouse 80), Murray, Sweeney, Franks (Holden 89); Howard, Poole (James 74). Subs: Austin, Humphreys, Walton, McHugh
SHREWSBURY TOWN: Weale; Grandison, Jones, Hector, Jacobson; Parry, Summerfield, Richards, Wildig; Gornell (Wright 76), Morgan. Subs: Anyon, Purdie, Taylor, Hall, Doble, Goldson.
Referee: Carl Boyeson (Hull).