Chelsea suffered frustration at the hands of determined Blackburn as the Blues were held at Stamford Bridge.
Chelsea's Andriy Shevchenko is frustrated after a first-half miss
Blackburn keeper Brad Friedel kept Chelsea at bay with a fine save from Michael Essien and a vital late block from Andriy Shevchenko.
Chelsea were furious when Salomon Kalou's 57th-minute close-range finish was controversially ruled offside.
Petr Cech saved well from Robbie Savage, while Blackburn lost defender Christopher Samba with a head injury.
Shevchenko was handed his first start of the season in place of Didier Drogba, who was ruled out with a knee injury.
And he wasted an opportunity to make an impression on Chelsea boss Jose Mourinho when the striker was let down by his touch after a pass from Essien, allowing Friedel to save at his feet.
Friedel had already saved brilliantly from Essien after 26 minutes, diving high to his left to turn away a rising 25-yard drive.
Blackburn coped well with Chelsea's first-half threat and almost snatched a shock lead after 41 minutes when David Bentley's right-wing cross found Morten Gamst Pedersen at the far post but his volley hit the side-netting.
David Dunn was only narrowly off-target with a speculative long-range effort as Chelsea continued to suffer real frustration.
And Mourinho made a double change after 56 minutes, sending on Mikel Jon Obi and Florent Malouda for Steve Sidwell and the subdued Shaun Wright-Phillips.
Chelsea were furious seconds later when Kalou turned in Juliano Belletti's cross, only for the goal to be harshly ruled out for offside.
Blackburn's confidence was growing as the second half went on and keeper Cech was called into action to turn over a 20-yard drive from Savage.
Shevchenko should have put Chelsea ahead with five minutes left, heading Malouda's cross straight at Friedel from point-blank range.
Blackburn defender Samba completed the clearance but at some cost because he was carried off after he was accidentally kicked in the head by Shevchenko.
Referee Howard Webb played eight minutes of injury time and Blackburn survived some anxious moments to celebrate a point at the final whistle.
Chelsea boss Jose Mourinho:
"Only the referee and linesman can explain why they made the decision to disallow the goal.
He added: "We played without scorers Didier Drogba, Claudio Pizarro and Frank Lampard - that's a big thing."
Rovers boss Mark Hughes on Samba's injury:
"I hope it's just a knock and Christopher will be groggy just for a couple of days.
He added: "We know we're a good side at this level.
"We've come here and set out our stall and made sure we didn't go under. Maybe we would have a couple of seasons ago."
Chelsea: Cech, Belletti, Alex, Terry, Ashley Cole (Ben-Haim 88), Wright-Phillips (Malouda 57), Sidwell (Obi 57), Essien, Joe Cole, Kalou, Shevchenko.
Subs Not Used: Cudicini, Ferreira.
Booked: Joe Cole, Belletti.
Blackburn: Friedel, Emerton, Samba (Ooijer 90), Nelsen, Warnock, Bentley, Savage, Dunn (Mokoena 81), Pedersen, McCarthy (Roberts 68), Santa Cruz.
Subs Not Used: Brown, Derbyshire.
Booked: Warnock, Savage.
Ref: Howard Webb (S Yorkshire).