Two efforts from striker Marvin Morgan looked like securing Shrewsbury a first away win back in League One, before substitute Monkhouse struck with time running out.
Pools, thumped 5-0 at Preston in midweek, took took a 15th-minute lead. Evan Horwood picked out Steve Howard and his header teed up Jon Franks to drill in his second goal of the season from 20 yards.
Home keeper Scott Flinders had to make a fine save to deny Matt Richards a quick leveller, but he was soon beaten when a long free-kick from Joe Jacobson fell kindly for Morgan to confidently net from 12 yards.
The secondhalf took an age to get going, but with seven minutes to go, the Shrews scored.
From a swift counter-attack from one penalty area to the other, Morgan got in behind the back four to roll his low finish into the net.
But they could not hold on and when a long ball was headed on by Howard it sat up for Monkhouse to crack in from 10 yards.