It prevented the Londoners taking over at the top of the Premier League table from Manchester United, who had beaten Liverpool earlier in the afternoon to themselves replace Arsenal at the summit.
El-Hadji Diouf was the Blackburn goal hero with a 70th minute headed equaliser after Didier Drogba had given Chelsea a fifth minute lead.
Blackburn, looking for their fifth successive home win, brought in Jason Brown for injured goalkeeper Paul Robinson, while teenage central defender Phil Jones was given his league debut and produced a man-of-the-match performance alongside Chris Samba as skipper Ryan Nelsen and Gael Givet both missed out through injury.
Third-choice keeper Ross Turnbull continued in the Chelsea goal while Michael Ballack was missing through injury.
Chelsea wasted no time declaring their intentions after Manchester United's win earlier in the afternoon as they surged in to the lead with just five minutes gone.
Nikolas Anelka ran in from the right and proved the ideal cross for leading scorer Drogba to fire the Blues ahead with a first-time left-foot drive from the edge of the 18-yard box.
Chelsea kept the pressure on and earned two corners in succession soon afterwards, with Salomon Kalou heading over from the second.
Rovers earned their first corner of the game on 16 minutes when a 25-yard free kick by Morten Gamst Pedersen was turned round a post by Turnbull.
Rovers gave as good as they got for much of the rest of the first half but Chelsea's lead rarely looked troubled.
As the interval approached, Chelsea lost Branislav Ivanovic with a leg injury, with Yury Zhirkov coming on as substitute.
Blackburn made a lively start to the second half, with Zhirvov blocking a close-range header from Croatian striker Niko Kalinic before Pedersen shot over.
It was Rovers who won the first corner of the second half while at the other end a cross from the right by Anelka produced a full-blooded challenge for the ball in the six-yard box between Drogba and Samba, with both players briefly requiring treatment.
Gritty Blackburn were making Chelsea battle all the way to hold onto their lead and on 70 minutes they were level when a pinpoint cross from the right by Michel Salgado was headed in at the far post by Diouf.
Chelsea piled on the pressure in the closing stages but the Blackburn defence held firm.