Carlisle took a fourth-minute lead when left-back Matty Robson lashed home a fine low shot from 20 yards which flew past home goalkeeper Sam Walker and into the back of the net.
Lee Miller nodded wide for the visitors from eight yards before Mark Gillespie saved Jabo Ibehre’s fierce effort and Colchester youngster Tosin Olufemi’s curling, first-time shot rattled the crossbar as the contest continued to ebb and flow.
Miller and Robson both went close for Carlisle as did Ibehre for Colchester, for whom Sanchez Watt fired just wide early in the second half before Craig Eastmond also went close.
Walker had to save Miller’s shot at his near post and the visitors then had a goal chalked out for offside after Liam Noble had put the ball in the net.
Gillespie palmed Sears’ shot over before Sears levelled with 19 minutes to go when he blasted home a half-volley after Gavin Massey had controlled Watt’s clever pass.
Gillespie palmed over substitute Alex Gilbey’s header late on as the points were shared.