Three goals in five second half minutes saw Rovers lose a nervy encounter at Anfield 2-1.
After a first 45 in which Paul Robinson kept Liverpool at bay with three outstanding saves, the game sprang into live after the restart.
Defender Sotirios Kyrgiakos opened the scoring on 48 minutes when he rose unchallenged to meet a Steven Gerrard corner kick.
But Rovers hit back straight away when El-Hadji Diouf's shot was diverted into the back of his own net by Jamie Carragher.
Sam Allardyce's side couldn't keep the scores level for too long and 90 seconds later Fernando Torres gave the home side he lead once again, firing home from close-range.
As a nervy Liverpool retreated Rovers grew in confidence but despite enjoying plenty of the ball in the final twenty minutes they lacked that killer touch to find an equaliser.
The re-introduction of David Dunn to the starting eleven was the only change made by Sam Allardyce from the side that drew 0-0 with Sunderland at Ewood Park last Monday night.
With Ryan Nelsen failing a fitness test on a thigh strain, it meant Phil Jones going back to the centre of defence to replace the suspended Chris Samba, Dunn moving into the middle behind Niko Kalinić.
The home side started as brightly as the late October sunshine, with Rovers having Paul Robinson to thank for a series of first half saves.
On eight minutes Fernando Torres spread play wide to the right for Maxi Rodriguez, the Argentine firing the ball low into the area for Joe Cole to shoot at point-blank, but Robinson stuck out a leg to brilliantly save. Raul Meireles could have done better on the rebound as he put his effort wide.
Balls into the Rovers box from wide gave the Anfield club their best chance of joy. Robinson again denying the home side, pushing aside a Sotirios Kyrgiakos header from Steven Gerrard's corner kick.
Rovers rarely threatened, but from their first corner kick of the game a quick break from Liverpool lead to yet another Robinson save. Gerrard broke at pace from Reina's quick throw, out wide to Lucas then to Meireles, he swept it back to Gerrard but Robinson flung himself full length to his left to turn the ball around the post.
Referee Phil Dowd then took centre stage by booking both Givet and Salgado for dissent after a generous free-kick given to Gerrard. That prompted manager Sam Allardyce to leave his post in the Director's Box to join the remonstrations on the touchline.
Rovers were hit with a blow on the half hour with Steven Nzonzi pulling up with what looked like a hamstring strain, Vince Grella, surprisingly named on the bench for the game, coming on to replace the Frenchman.
Michel Salgado brilliantly blocked a shot from Meireles, whilst Lucas headed over when well placed in the six yard box. Then at the end of the half Brett Emerton couldn't make the most of a rare opportunity after Skrtel and Konchesky got in each other's way.
The second half couldn't have started any worse as Rovers went a goal down just two minutes after the restart.
Greek defender Kyrgiakos had been a threat from corner kicks all afternoon, and as Gerrard swept the ball in from the left, the Liverpool man headed home despite Martin Olsson's best efforts on the line.
But Rovers hit straight back and it was in no small part to half time substitute Benjani.
On for Kalinić, Benjani rounded the back of the Liverpool defence to hit the ball across the area where El-Hadji Diouf turned and shot goalwards. Konchesky looked to clear on the line only for the ball to strike Jamie Carragher and deflect into the back of the net.
The joy at equalising would only last two minutes as a third goal in the space of five minutes was scored. Joe Cole sending the ball in for an unmarked Torres to fire back across goal past the helpless Robinson.
The Rovers players and bench were furious that the goal was allowed to stand, as Martin Olsson was down in the area with a head injury and with Torres looking a yard offside when he scored.
Junior Hoilett replaced David Dunn on 67 minutes as Rovers looked for a way to get back on level terms. Morten Gamst Pedersen not too far away with an ambitious half-volley that the Norwegian swept goalwards.
As the home side retreated, Rovers grew in confidence but despite pushing Liverpool back, seeing plenty of possession and threatening with balls into the area, more couldn't be made of the opportunities.
The Anfield crowd grew increasingly nervous as the clock ticked down, Liverpool showing their intentions by keeping the ball in the corner rather than attempt a shot on goal from a late free-kick.
Liverpool held on to claim the points, leaving Rovers just ahead of their opponents on goal difference in the league table.
LIVERPOOL: Reina, Konchesky, Meireles (sub Shelvey 89 mins), Gerrard (c), Torres, Cole (sub Ngog 79 mins), Kyrgiakos, Rodriguez, Lucas, Carragher, Skrtel.
Subs not used: Jones (GK), Jovanovic, Babel, Poulsen, Kelly.
ROVERS: Robinson (c), Salgado, Jones, Givet, Olsson, Emerton, Dunn (sub Hoilett 67 mins), Nzonzi (sub Grella 33 mins), Pedersen, EH Diouf, Kalinić (sub Benjani 46 mins).
Subs not used: Bunn (GK), Morris, Chimbonda, MB Diouf
Booked: Rodriguez, Meireles (Liverpool), Givet, Salgado, Grella (Rovers).