Daniel Powell, Darren Potter and Samir Carruthers all flashed half-volleys narrowly wide as the Dons controlled a subdued first half-an-hour.
But Guy put Carlisle ahead after 35 minutes when he swivelled to volley the ball high into the net after David Amoo had knocked back Conor Townsend’s deep cross.
Carruthers had a long-range curler tipped over the bar by Mark Gillespie as the hosts battled back, while Brad Potts poked tamely at Dons keeper Ian McLoughlin one-on-one on the stroke of half-time.
The Cumbrians almost extended their lead seven minutes after the break when Townsend glanced a diving header wide from Matt Robson’s excellent cross.
The lacklustre Dons probed for an equaliser in the closing stages but substitute Izale McLeod and Patrick Bamford both planted headers narrowly wide as they slipped to their third defeat in four games.