Bottom club Pools looked to be heading for yet another defeat when Gary Roberts set up Simon Ferry for Swindon's opener in the 15th minute.
But Town failed to make the most of their dominance and it needed a top-class save from Wes Foderingham to deny James Poole an equaliser.
Hartlepool goalkeeper Scott Flinders made an outstanding triple save to deny Adam Rooney, twice, and Roberts.
And Swindon paid for their wastefulness when Jonathan Franks headed into the danger area after 75 minutes and Monkhouse supplied the finishing touch.
Monkhouse had only been on the pitch 13 minutes after replacing Poole as manager John Hughes tried to find a way back into the match.
Swindon fans, meanwhile, chanted the name of manager Paolo Di Canio, who had recently said he was considering his future at the Wiltshire club.
Swindon last week