Eidur Gudjohnsen looked to have returned to haunt his former club with a 58th minute strike to put Barca in the lead before Drogba scored his fifth goal in four European games to earn Jose Mourinho's side a precious point.
In between, Gudjohnsen was stretchered off after falling awkwardly following a challenge with Ricardo Carvalho and the result leaves Barcelona's hopes of progressing still hanging by a thread as they slipped to third place in the Group A table.
Barcelona started in positive fashion and took the lead after just three minutes.
Slack defending by Khalid Boulahrouz gifted possession to Deco and he scampered down the left wing before cutting inside and smashing a low right-foot shot past the despairing dive of Henrique Hilario in the Chelsea goal.
Ronaldinho should have made it two seconds later when he drilled over the top after excellent wing play from Lionel Messi.
Xavi was then denied by Hilario after the Spain international combined superbly with Ronaldinho and struck a first-time effort from 15 yards that the keeper palmed to safety.
Despite being under the cosh, Chelsea began to grow in confidence and, after Victor Valdes tipped over a powerful Michael Essien header and palmed away a crashing drive from Arjen Robben, the visitors pulled themselves back on level terms.
Frank Lampard looked to have mis-controlled the ball in the box but, from a near impossible angle, scooped the ball over the head of Valdes and under the crossbar to silence the Nou Camp.
But Frank Rijkaard's side refused to be downbeat and restored their advantage on 58 minutes through Gudjohnsen.
Ronaldinho skinned Boulahrouz with a quick flick and stabbed the ball into the six-yard box for Gudjohnsen to slot home from close range.
Soon after Lampard went down in the box under a challenge from Xavi but Chelsea's penalty appeals were rejected by the referee who was kept busy on the night by a string of tetchy fouls and a constant stream of yellow cards.
Michael Ballack then wasted a glorious chance to equalise with a wild shot over the bar before Drogba struck in the 92nd minute.
Terry headed the ball back into the danger area and the Ivory Coast striker controlled on his chest and rounded Rafael Marquez before stabbing home from close range amid scenes of wild jubilation on the pitch and also the Chelsea bench.