On a Brunton Park pitch with more mud than grass the ex Premiership striker provided the only touch of class with just 15 minutes to go.
Chris Lumsdon stroked a perfect pass to Bridges, who danced past Alan Marriott and held off Colin Cryan to finish for his 12th of the season.
Before the goal both sides had hit the crossbar in an absorbing encounter.
First it was Bridges after 20 minutes who took advantage of some loose defending to curl a 20-yard effort onto the bar and over.
Early in the second half Marvin Robinson turned Danny Livesey inside out, but with just the keeper to beat he also hit the woodwork.
Neither side dominated and with few clear-cut chances both sides resorted to long shots.
Karl Hawley and Bridges both went close from distance, while Luke Foster fired over for the Imps.
Robinson should have done better for the visitors late in the first half, but his far-post header was weak allowing Keiren Westwood to save easily.
With tempers fraying as the game wore on Foster and Lumsdon were both booked for fouls.
But Bridges' strike eased the pressure on the Cumbrians and as Lincoln pushed forward they left space behind.
United striker Derek Holmes should have scored from 12 yards before Imps sub Jude Stirling was booked for a wild lunge at Bridges.
Gary Birch almost levelled spectacularly with the last kick for the Imps, but it was Carlisle's day for a sixth straight league win.