The host had to twice come from behind in an entertaining match which was not without incident producing both a penalty and a disallowed goal.
The home fans had to wait until the 74th minute for the debut of Chelsea's latest signing Argentinian striker Hernan Crespo bought in midweek for £16.8million, but ultimately he was not able to influence the result.
The game began in sensational fashion with Rovers' Andy Cole scoring within the first minute. The Blues were left shaken after captain Marcel Desailly's mistake on the touchline.
Desailly struggled to keep the ball in only for it to be stolen by Matt Jansen, whose pin-point accurate cross found Cole who obligingly struck home.
Jansen, Cole and Steven Reid continued to create problems at the back for Chelsea in the opening 25 minutes.
The home side found short lived joy after 30 minutes when neat build up saw Adrian Mutu take a deft pass from Geremi and find the net. But the celebrations were premature because the far side linesman had seemingly ruled Mutu offside.
After the match Chelsea manager Claudio Ranieri questioned the linesman's slow response time in making the call.
In the ensuing counter-attack Blackburn almost doubled their lead but David Thompson's curling shot went wide.
Chelsea finally found an equaliser in the first minute of first-half injury time when Mutu took a through ball from Frank Lampard. He just managed to evade the advancing Blackburn keeper Brad Friedel and defender Lucas Neill arrived too late to block the shot.
Eleven minutes into the second half the visitors went ahead again and again it was thanks to Cole. Chelsea failed to clear a corner and keeper Carlo Cudicini missed an attempted punch. Cole was lurking on the far post and although off balance steered the ball cleanly in for a 2-1 advantage.
The controversial penalty that allowed Chelsea to draw level came five minutes later as Geremi took the ball to the penalty box. He attempted a high cross but the ball flew straight towards Neill, hitting his arm.
Referee Mike Dean pointed to the spot and Jimmy Floyd Hasselbaink sent Freidel the wrong way to convert.
Rovers manager Graeme Souness described the penalty as: "Very, very harsh." He said Neill had raised his right leg and the arm had just followed it instinctively.
Souness seemed happy enough to go away from the Bridge with a point: "You're not going to come here and not be under pressure.
"We took our opportunities and defended well although I would have liked more of the ball than we had."As for Cole's double he said: "The striker had had a bad year by his own standards last year, but was hopeful of an improvement this season. He's got the bit between his teeth at the moment, we have goy to keep it there."Ranieri also did not seem to perturbed by the result although it ends his team's winning streak and means Chelsea have still not beaten Blackburn at home in the Premiership.
He labelled Blackburn's goals as: "Two big presents" and said Chelsea had to stop giving away such presents.
Replacing Damien Duff at half time had been a tactical move he said, it was not forced by injury.