Both keepers had made fine saves at the same end of the ground, before Xabi Alonso stroked home the opener midway through the second half.
Yossi Benayoun added a skilful second ten minutes later, before Roque Santa Cruz rediscovered his goalscoring touch to give the home fans some hope.
But Steven Gerrard sealed the win with the last kick of the game to extended Rovers' winless run in the league to ten games.
Before the game, both managers made three changes to the sides from their last outings, with Santa Cruz and Brett Emerton passed fit for the hosts, while Robbie Keane and Albert Riera were both relegated to the visitors' bench.
And the game's first two chances fell to players returning to their starting line-ups.
On 19 minutes, Dirk Kuyt played in Benayoun, but former Liverpool full-back Stephen Warnock recovered just in time to make a goal-saving tackle.
And ten minutes later, Gerrard, who was guilty of giving possession away on numerous occasions in the first half, passed the ball straight to Morten Gamst Pedersen, who let fly from fully 25 yards, only for Pepe Reina to terrifically tip the ball onto the bar.
Pedersen fancied his chances from even further out a little later, firing in a 30-yard free-kick, which Reina had to palm around the post.
The final chance of the half dropped to Gerrard, who lashed a left-foot shot well wide of the target.
The visitors provided more of an attacking threat in the second half, with Paul Robinson twice coming to Rovers' rescue.
On 57 minutes, Emiliano Insua's cross fell kindly for Alonso, whose crisp strike was well kept out by the England international.
And five minutes later, Gerrard's effort was superbly saved by the Robinson and Benayoun just couldn't force home the follow-up.
But with little over 20 minutes remaining, the league leaders eventually made the breakthrough. Gerrard picked out Kuyt, whose shot was blocked by a couple of Rovers bodies, but Alonso was on hand to stroke home the rebound.
Rovers had an excellent chance to equalise when Andre Ooijer picked out Santa Cruz in the centre, but the Paraguayan striker sent his free header well wide.
And the home side were made to pay for the miss, as Liverpool extended their lead with their next attack. Kuyt played a superb volleyed pass out wide to Benayoun, who skipped past Warnock before drilling the ball under Robinson.
Rovers did get a goal, which their steely endeavour deserved, but it proved too little too late. A corner from the right was swung in by Keith Andrews, Ooijer flicked on and Santa Cruz headed home at the far post.
There was still time for Liverpool to add a third, when Robinson came rushing out of his goal to deny substitute Nabil El Zhar. Alonso squared the loose ball to Gerrard and the skipper slotted the ball into the empty net.