The brilliant Steven Gerrard scored one and made another for Fernando Torres before substitute Andrei Voronin sealed an impressive display with a late third goal.
Roque Santa Cruz grabbed a stoppage-time consolation goal for Mark Hughes' men.
With Everton dropping points against Birmingham City on Saturday, the Reds had a golden opportunity to open up a five-point gap in the race for the fourth Champions League spot.
And they should have been ahead after eight minutes when Gerrard's corner found an unmarked Torres only for the prolific Spaniard to nod wide from six yards out with the goal gaping.
Ten minutes later Gerrard went down under a challenge by Rovers keeper Brad Friedel but referee Alan Wiley waved away the penalty claims as the away fans held their breath.
Blackburn offered little in the early stages as Liverpool poured forward at every chance.
Gerrard was at the heart of everything and the skipper appeared to be pushed over on the edge of the area by Christopher Samba after another surging run on 25 minutes but again Wiley ruled no foul to a roar of disapproval from The Kop.
Then a flowing Liverpool move saw Dirk Kuyt and Torres combine to release Gerrard only for the midfielder to scuff his shot wide.
It was half-an-hour before Rovers carved out their first chance when a clever David Bentley pass found Santa Cruz but Jose Reina got down well to save his shot.
But it was Rafa Benitez's men who were creating the better chances and they had another chance to open the scoring through Kuyt five minutes before the break only for the Dutchman to inexplicably head Gerrard's cross wide at the far post.
Chances were scarce after the break as both teams started the second half slowly.
The game was in desperate need of inspiration before Benitez pulled off the ineffective Ryan Babel for Yossi Benayoun on 58 minutes. It proved to be an inspired substitution from the wily Spaniard as two minutes later his side took the lead.
Gerrard weaved his way through the Blackburn defence, played a neat one-two with Lucas Leiva and coolly slid the ball under the diving Friedel to finish off an exquisite move.
Blackburn had no answers as the Reds cut through their defence at will after that and with eight minutes left it was 2-0.
Again the brilliant Gerrard was involved, latching onto to a poor pass from Stephen Warnock and crossing for Torres to plant a precise header into the corner of the net.
Substitute Voronin capped off an impressive Liverpool display by sliding in to score from John Arne Riise's cross before Santa Cruz grabbed a late consolation goal for Blackburn with a volley that fizzed past Reina.