Leeds were looking to kick on from their midweek win over Blackpool and an unchanged side enjoyed the bulk of possession as well as creating the best chances.
But Rovers, who suffered their first defeat in seven games at Hull on Tuesday, held firm to climb one place up the Championship ladder to 10th, directly below Leeds.
It was the visitors who were on the front foot from the first whistle and Grant Hanley twice had to throw himself in the path of shots from Ross McCormack.
Tom Lees was well-placed when he connected with a McCormack cross but his effort was easily dealt with by Jake Kean before another Hanley block denied Steve Morison with Luke Varney shanking the rebound wide.
Paddy Kenny was finally called into action on the half hour when Colin Kazim-Richards collected a Danny Murphy pass before drawing a low save from the Leeds goalkeeper.
Possession was shared evenly for the remaining 15 minutes of the first half but neither side could muster any chances of note.
McCormack should have put the visitors in front two minutes after the restart after Varney and Morrison combined to tee him up in the Blackburn box only for the striker to fire into the side-netting.
And Jordan Rhodes was guilty of an equally poor effort just after the hour after Murphy dispossessed Lees and put the Rovers man through on goal but he fired wide with only Kenny to beat.
The game opened up in the final stages and Scott Dann almost put through his own net trying to steer a McCormack cross behind.
There were further chances for Varney and Rhodes but both were dealt with easily by Kean and Kenny respectively while Morten Gamst Pedersen headed wide at the death.