The goal seemed to stun Carlisle and Monkhouse could have scored a second for the visitors when the Carlisle defence froze, but he blasted over from 20 yards. The defeat means Carlisle have now picked up just one point from a possible 27.
Under-fire manager John Ward rang the changes in the aftermath of Saturday's 5-0 thrashing at Colchester. Wingers Simon Hackney and Cleveland Taylor didn't even make the bench as United tried to shore up the midfield.
John Welsh, on loan from Hull City, started the game and mopped up in front of the back four. The tactics appeared to be working as Carlisle had the lion's share of possession but created few decent scoring chances. David Raven got forward got forward as early as the fifth minute, but there was no killer touch to his ball across the face of goal.
Good link-up play by Raven and Graham Kavanagh had Hartlepool in a fluster but Jeff Smith could only force a 23rd minute corner. A minute later patient build-up play could have paid dividends when Evan Horwood's cross was only partially cleared, but Arran Lee-Barrett wasn't troubled in collecting Danny Carlton's header.
The Cumbrians' best effort fell to top scorer Danny Graham in the 78th minute when Sam Collins gifted him a sight of goal, but the keeper kept out his shot. Carlisle pressed hard for the equaliser and substitute Jennison Myrie-Williams cut inside, but his shot deflected over the defender into the arms of the keeper.
Brown was only just wide with a curling shot just inside the box for Hartlepool and at the death two stunning saves by Alnwick prevented the visitors from adding to their lead. Carlisle's eighth league defeat in nine games further heaping the pressure on beleagured boss John Ward.