The 27-year-old ex Leeds and Newcastle hit man picked up Adam Murray's 80th minute pass before rounding keeper Matthew Gilks and despite the best efforts of Warren Goodhind, Bridges rolled the ball easily into the empty net.
Rochdale were left scratching their heads as to how they didn't win, but in truth the home side were simply the better of two poor teams.
The Cumbrians almost took the lead within 30 seconds but Peter Murphy's 40-yard free kick was well saved at the second attempt by Gilks.
Dale hit back immediately when Paul Tait set up Blair Sturrock to fire in low past the despairing Keiren Westwood with just 1 minute 22 seconds on the clock.
Sturrock could easily have put Dale out of Carlisle's reach with two golden chances.
First he blasted narrowly over from 12 yards and 60 seconds later his long-range angled drive was only just dealt with by the nervous Westwood.
Bridges and Murray both went close for Carlisle but it was the visitors who dominated on a pitch that would have been more at home to a Rugby League game.
Carlisle struggled to deal with Rochdale's long ball game and Danny Livesey's equaliser came as a shock to both sides.
Bridges should have scored but took a touch too many before being tackled.
From the resulting corner Kevin Gray slammed a header against the bar and Livesey reacted quickest to prod home from close range.
Rochdale came back strongly and had Carlisle pinned in their own half for long periods, but despite their domination could not find a clear-cut chance.
But Bridges' late strike broke Rochdale's heart and despite their best efforts Steve Parkin's side could not get themselves back in the game.