The Ewood Park outfit also enjoyed a moment of good fortune when referee Howard Webb controversially disallowed a Salomon Kalou effort for offside in the second half.
Rovers almost stole all three points late in the game through Robbie Savage but this result extends Mark Hughes's unbeaten run to 15 games in all competitions.
Hughes insisted the officials had got the decision right but preferred to shift the focus to his side's defensive efforts.
"The lad is offside at the time (of the pass)," said Hughes on Setanta Sports .
"I'm sure the Chelsea bench were up in tandem but you hope to get a break in the game and if we'd have conceded then it would have been very difficult to get back.
"The qualities we showed after that proved the strength we have here.
"It's a great spirit within the group, the refused to go under.
"At the end of the game John Terry and everybody seemed to be in our box and we showed a real mentality at that stage."
Rovers hero Brad Friedel believes his team-mates will be content with the result but was not happy with the method.
"We'd have taken a draw at the start of the day but we didn't enjoy how we played. Today's game, out of all the games this season in the Premier League and in Europe, was the worst we've played."