Blackburn and Liverpool shared the points in a tightly-contested match.
Dunn hit the woodwork for Rovers in the first half
Rovers should have been in front by the interval after twice hitting the woodwork through David Bentley's effort and David Dunn's wonderful shot.
The game was more even in the second half, and both Christopher Samba and Dirk Kuyt could have done better for the visitors in promising positions.
Late on Brad Friedel twice saved Steven Gerrard shots, Peter Crouch went close with a header and Kuyt missed badly.
Liverpool deployed Kuyt as a lone striker, though Gerrard tried to get forward in support as often as possible.
But with Ryan Nelsen and Samba getting the better of the Dutchman, who has failed to score a league goal in open play this season, Liverpool struggled once the ball reached the Blackburn area.
Liverpool's wide players, Yossi Benayoun and Ryan Babel, also found the going tough - as did Blackburn's wingers Morten Gamst Pedersen and Bentley.
And with the play congested in midfield, both sides laboured to create scoring opportunities.
Finally after 34 minutes Blackburn did just that - and came desperately close to scoring - as Pedersen and Bentley came infield to link up well.
Bentley collected Pedersen's flicked header and his low shot grazed the foot of Jose Reina's post.
Four minutes later the game was treated to its first meaningful save when Friedel threw himself to his left to push away Babel's powerful shot.
Just before half-time Dunn was desperately unlucky not to score when his superbly executed shot crashed off the bar.
Dunn limped off at the end of first period and although he re-emerged for the second half he was soon to be replaced by Tugay.
The game was more open up after the interval and Samba might have done better when John Arne Riise failed to clear, but the Blackburn defender delayed his shot.
Just past the hour Kuyt failed to pick the right pass with Gerrard in wonderfully promising position.
Gerrard then drew two fine saves from Friedel, while substitute Crouch had a header cleared off the line by Bentley.
In the closing minutes Kuyt missed a glorious chance after good work by Harry Kewell and the Dutchman then went close with an angled shot.
Blackburn manager Mark Hughes:
"It was a very good game. There were a number of chances for both teams. There were clear cut chances that on another day would have gone in.
"It was an evenly-matched game. But the last ten minutes were difficult for us.
"Liverpool had a number of chances and our keeper Brad Friedel did well for us when we were tired."
Liverpool boss Rafael Benitez:
"I am disappointed. We deserved to win. We created very, very clear chances - and plenty of them.
"When the game became more open we had more control and went forward. We had more offensive players.
"We must think about the positives, we had a lot of possession and a lot of chances. In the second half, their goalkeeper was their best player."
Blackburn: Friedel, Ooijer, Samba, Nelsen, Warnock, Emerton, Bentley, Dunn (Kerimoglu 56), Pedersen, Santa Cruz, McCarthy (Derbyshire 89).
Subs Not Used: Brown, Khizanishvili, Treacy.
Liverpool: Reina, Finnan, Carragher, Hyypia, Riise, Benayoun (Crouch 72), Sissoko, Mascherano, Babel (Kewell 63), Gerrard, Kuyt.
Subs Not Used: Martin, Arbeloa, Lucas.
Ref: Martin Atkinson (W Yorkshire).