Chelsea must win it to stay in it. Champions League qualification was always a distant hope through the Premier League for Roberto Di Matteo but, as though the club's first European Cup was not incentive enough, there is no alternative now but to beat Bayern Munich in their own backyard after the lowest league finish of the Roman Abramovich era was confirmed at Anfield.

A top-four finish was obliterated from the equation for Chelsea by a rampant Liverpool team swaggering with a self-belief and adventure absent from their FA Cup final display at Wembley three days previously.

Kenny Dalglish's biggest league win of the season arrived too late to alter the complexion of the club's season but, with Andy Carroll again a dominant force and an impressive home performance reflected in goals for a change, Liverpool signed off at Anfield with a flourish and a flicker of hope.

Chelsea departed in the sure knowledge that several players had ruined their prospects of starting at the Allianz Arena but with minds focused. Given the trials that preceded Di Matteo's appointment as interim manager nine weeks ago, following the dismissal of André Villas-Boas, win or bust at the Allianz Arena is an acceptable return.

A repeat of this ramshackle defensive display on Saturday week, however, and the Kop's taunt of "Bayern Munich, they'll win it five times" will ring true.

The visitors arrived with their Premier League campaign alive but the night was not without incentive for Liverpool, however demoralised the club may have been by Saturday's defeat and their performance against the same opponents in the FA Cup final.

Victory avoided equalling the lowest return of home wins in a top flight campaign at Anfield – the five of 1948-49 – maintained hope of finishing above Everton in the table and restored some optimism ahead of Dalglish's end-of-season review with the club's owners. Against another team Liverpool might have struggled to rouse itself but not against Chelsea and not against a side containing Fernando Torres, back on Anfield soil for the first time since his acrimonious £50m exit 16 months ago.

The obligatory boos reverberated around Anfield every time the Spain international touched the ball. Torres must have been tempted to join in, such was the paucity of the performance around him and particularly of a visiting defence destroyed by the channelled aggression of Carroll and skill of Luis Suárez.

Di Matteo made eight changes to the team that began at Wembley but the rotation policy that has served him so well of late failed him here. Even so, he had every right to expect more from John Terry, his captain, and Branislav Ivanovic in central defence although, in mitigation to the established pair, they were exposed frequently by those around them, including Ross Turnbull in goal. Chelsea started strongly and should have opened the scoring when Ivanovic planted a free header from Florent Malouda's corner against a post.

But, unlike at the Cup final, Liverpool showed up from the first whistle. Out of the ashes of their misery the Liverpool manager had urged his players to find confidence in their rousing finale at Wembley and they stunned Di Matteo's makeshift team with three goals in nine remarkable minutes. From a Chelsea perspective all three were easily avoidable.

Suárez engineered the first when he held off Oriol Romeu down the right wing, nutmegged the Chelsea captain as he entered the area and cut the ball back into Michael Essien who diverted it into his own goal.

A slip by Terry as he moved to collect a pass from Maxi Rodríguez enabled Jordan Henderson to go through on goal and beat Turnbull with a cool finish into the bottom corner and then, with the Chelsea keeper AWOL at a Jonjo Shelvey corner, Daniel Agger glanced Carroll's header into the unguarded net.

Torres's duel with the recalled Jamie Carragher simmered nicely and the Chelsea forward was denied another goal in front of the Kop when his angled drive cannoned off the underside of the crossbar. At the other, busier, end Carroll was thwarted by Turnbull as he cut into the area and Stewart Downing struck the bar with a delightful volley from Suárez's knock-down.

The moment for Downing to break his Premier League duck for Liverpool arrived on the stroke of half-time when Ivanovic conceded a ludicrous penalty for elbowing Carroll in the chest as they awaited Henderson's cross.

Ivanovic was only booked but, from 12 yards and having sent Turnbull the wrong way, Downing smacked his spot-kick against the post and out. Liverpool's seventh penalty miss of the season set an unwanted club record and extended their number of strikes against the woodwork to 46.

Chelsea were being embarrassed and responded at the start of the second half when Ramires unwittingly bundled Malouda's inviting free-kick beyond José Reina. But any thoughts of a recovery ended when Turnbull scuffed a hopeless clearance into the path of Shelvey and the Liverpool midfielder drilled the return high into his unguarded net.