David's Bentley and Dunn both struck the woodwork for the home side, who dominated for long spells.
But they had to hold firm at the back to claim another impressive point, as Liverpool threw everything forward in a rousing finale.
Both sides enjoyed 2-1 Carling Cup victories in midweek, with Rovers making three changes to the side that defeated Portsmouth, while Liverpool made eight alterations to the side that saw off Cardiff.
There were fireworks flying over the hills behind Ewood, but there was little to excite the crowd in the opening half-an-hour.
Dunn registered the first effort of the game - a wayward left-foot shot on seven minutes - before Morten Gamst Pedersen saw a header and a long-range strike drift comfortably into the arms of Pepe Reina.
Dirk Kuyt cut a frustrated lone figure in the Liverpool attack, caught offside on numerous occasions in the opening period, while some flashes of Benni McCarthy magic were almost all there was to enjoy at the other end.
The best chance of the half arrived on 35 minutes courtesy of some neat one-touch football, which the Rovers fans have come to enjoy in recent weeks.
A long ball forward was flicked on by Roque Santa Cruz to Pedersen and the Norwegian in turn headed on to Bentley, who shrugged off the challenge of John Arne Riise before firing a left-foot strike onto the outside of the post.
On a cold evening in East Lancashire, Bentley then warmed the gloves of Reina with a crisp right-foot volley from outside the box, while at the other end, Steven Gerrard worked the ball left to Ryan Babel, who forced a fine diving save from Brad Friedel.
But Rovers were in control and, on the stroke of half-time, Dunn unleashed a stinging left-foot shot which cannoned off the underside of the bar, before being cleared to safety.
Fans' favourite Christopher Samba ensured the second half started brighter than the first.
After picking the ball up in midfield, Samba continued his run into the box, and when Pedersen's cross fell kindly for him at the far post, the giant defender's left-foot strike was deflected wide for a corner.
At the other end, twice Kuyt found himself bearing down on goal and twice the Dutchman rolled the ball comfortably into the arms of Friedel.
Rovers then almost broke the deadlock from successive corners. Andre Ooijer had appeals for a penalty waved away from the first, before Santa Cruz sent a free header over the bar from the second.
The Reds rallied late on, but failed to find the back of the net. On 79 minutes, Gerrard played a give-and-go with Kuyt, but Friedel stood up to the test against the Liverpool skipper. And from the resulting corner, Bentley kept out substitute Peter Crouch's header on the line.
As the final few minutes approached, Crouch laid the ball off to Gerrard, whose low drive was again parried by Friedel, while Kuyt wasted another two glorious opportunities from inside the box.