Carlisle issued an early warning to City's defensive line-up in the 8th minute, with Andy Preece heading Tom Cowan's right-wing cross against the post.
Stuart Elliott did likewise at the other end in the 33rd minute, crashing a shot against former City keeper Matt Glennon's near post.
Stuart Green had the last and possibly best chance of the half. Ben Burgess's pass put the midfielder through but he inexplicably shot wide as he bared down on Glennon's goal.
10 minutes into the second half, Tigers keeper Boaz Myhill made a great save from Paul Simpson's free kick, but the danger wasn't properly cleared and Andy Preece found himself free of his marker to squeeze a shot past Myhill and give Carlisle the lead.
Both sides were sloppy in the final thirds of the pitch in poor conditions for football. Ben Burgess hit the woodwork in the 75th minute, but ex-Carlisle player Stuart Green was the inevitable scorer on his return to Brunton Park to make amends for his earlier miss. Elliott pulled the ball back from the touchline, and Green slotted a shot past Glennon from 6 yards out to save a point.
City line-up (4-4-2): Myhill; Marshall, Whittle (Melton 65), Joseph, Dawson; Green, Hinds, Delaney, Elliott (Holt 84); Allsopp (Walters 60), Burgess.
Un-used subs: Musselwhite, Forrester.