A Steven Gerrard inspired Liverpool responded perfectly, after their last 1-3 defeat at home to Aston Villa, by notching a late comeback in their 3-2 win away at Bolton Wanderers.
But the visitors were made to fight desperately hard by a Bolton side who were down to 10 men for much of the second period.
Gary Megson's men had been ahead twice through Kevin Davies and Tamir Cohen, and Liverpool only really got on top when Sean Davis was dismissed for a second bookable offence.
Glen Johnson had fired one equaliser in the first half, before Fernando Torres pulled Liverpool level at 2-2 a couple of minutes after Davis angrily trudged off.
Then Gerrard struck with a fierce drive seven minutes from the end to lift at least some of the pressure from Benitez.
Bolton made one change from the side that won at Tranmere in the Carling Cup in midweek, with Tamir Cohen replacing Mark Davies.
Liverpool boss Rafa Benitez gave new Greek signing Sotirios Kyrgiakos his debut in place of Martin Skrtel, while Spanish winger Albert Riera replaced Yossi Benayoun on the left-flank.
And Riera soon knew he was in a game as he was clattered by a strong Sam Ricketts tackle and then collected the Welsh international's boot in his ribs minutes later.
But Liverpool soon had chances as Riera's cross was missed 12 yards out by Lucas, and the ball was returned into the box by Johnson for Fernando Torres to see a glancing header skim wide.
Torres was next, cut down by Gary Cahill, with the defender one of three Bolton first-half bookings, the others being Davis and Muamba.
The visitors had plenty of possession, but without making many clear-cut chances, Matt Taylor and Cohen working tirelessly in midfield, breaking up Liverpool's flow.
One through-ball from Lucas saw Torres shake off Cahill and attempt to chip Jussi Jaaskelainen from just inside the box, but the goalkeeper pulled down the effort.
At the other end, a Taylor free-kick was headed away for a corner by Torres, and that gave Bolton their breakthrough.
Taylor's 32nd-minute corner curled to the far post where Johan Elmander headed it down into the six-yard box for Davies to turn past Jose Reina from a couple of yards.
Liverpool surged back looking for an equaliser, and it almost came when Torres chested down Johnson's cross, but fired it across goal and wide of the far post.
But the visitors were level in the 42nd minute when a corner was cleared only as far as Johnson just outside the box, and he fired a low show inside Jaaskelainen's near post.
Bolton caught Liverpool asleep at the beginning of the second period. Liverpool's failure to clear a right-wing cross saw them go behind again just two minutes after the break.
Davies was able to flick the ball across the box, where two defenders failed to stop Cohen lashing the ball home from eight-yards.
Bolton were reduced to 10 men after 54 minutes. Lucas was racing towards the Bolton box when Davis clipped his heels from behind. Referee Alan Wiley produced a second yellow and then the red card.
It was the incentive Liverpool needed. Gerrard hit the bar before Torres took a chest-down from Dirk Kuyt before steering the equaliser past Jaaskelainen in the 56th minute.
Not surprisingly, it was all Liverpool now. Andriy Voronin was sent on after 74 minutes to replace Javier Mascherano as the pressure on Bolton increased.
Torres and Kyrgiakos both had chances, and Bolton sent on another defender in Gretar Steinsson for Cohen with 12 minutes left.
Liverpool's pressure paid off with seven minutes left when Gerrard crashed the ball home from 12 yards. Benayoun's corner had been headed down by Torres for the Liverpool skipper to finally put his side ahead and it proved decisive.