The pendulum seemed to swing Chelsea's way when Ibrahimovic saw red for a clumsy challenge on Chelsea midfielder Oscar, but the visitors never gave up the fight against the side that knocked them out at the quarter-final stage last year.
They came storming back after Gary Cahill gave Chelsea the lead when he lashed home after 81 minutes and their never-say-die attitude was rewarded with four minutes of normal time to go.
Former Chelsea defender David Luiz scored with a powerful header from a corner that flew in off the underside of the bar to make it 1-1 on the night and force extra time.
The French side should have taken the lead after 58 minutes when Edinson Cavani rounded goalkeeper Thibaut Courtois, but he hit the inside of the near post.
Despite an electrifying start to the match that included an attempt from Cavani after two minutes, and end-to-end play, neither team actually had an effort on target in the first half.
Yet the football both were producing was ruggedly entertaining with Chelsea's Hazard creating opportunities for his front men which they could not capitalise on.