Manchester United have added to Liverpool's woes, as Bruno Fernandes' unstoppable late free-kick earned his side a 3-2 win in a blockbuster FA Cup fourth-round clash.
On as a substitute, the Portuguese stepped up to bend a right-footed strike beyond Alisson in the 78th minute to book a last-16 tie for his side against West Ham United.
Mohamed Salah scored both Liverpool's goals, the first to give his side an 18th-minute lead before Mason Greenwood levelled and then again in the 58th minute, after the outstanding Marcus Rashford had slotted United ahead.
Liverpool looked the more likely winners, but Fernandes, so often United's spark, sealed it with his 28th goal in all competitions for the club, since his debut last February.
The tie proved an absorbing tussle, in marked contrast to the turgid 0-0 Premier League stalemate between the sides at Anfield last weekend.
But that was of scant consolation for Liverpool, who have now won only once in seven games in all competitions.
"We played some really good stuff, good goals, we have to defend well against them and we managed to react well," United manager Ole Gunnar Solskjaer says.
Playing in their unfamiliar blue away kit, Liverpool looked much more like their old selves, as their misfiring forward line clicked back into gear.
They went ahead in the 18th minute in tried-and-tested style, Roberto Firmino slicing open United's defence with a superb pass to Salah, who dinked a cool finish over Dean Henderson.
United took only eighth minutes to respond. Paul Pogba won a tackle on the edge of his own box and Rashford advanced, before delivering a 'quarterback style' pass that Liverpool's James Milner failed to cut out.
The ball arrived at Greenwood, who took a touch, before burying his shot past Alisson.
Another Rashford raid just before the break ended in Pogba flashing a shot just wide, when he should have hit the target.
United were ahead shortly after the restart, when Greenwood slid in Rashford, who guided his shot past Allison.
Back came Liverpool, with Milner wasting a glorious chance to score, before Edinson Cavani sloppily gave away possession in a dangerous area and Firmino's ball in was dummied by Milner, with Salah snaffling the chance.
Both sides hunted the winner, but when Cavani was fouled on the edge of the area, Fernandes meted out punishment.
"When you leave him out like I did today, he stayed about 45 minutes after training yesterday, shooting free kicks, so I was pretty confident he could score one if he got the chance," Solskjaer says.
Leicester City 3 Brentford 1
Leicester City's James Maddison has set up one goal and got on the scoresheet in a second-half comeback, as they beat second-tier Brentford in the FA Cup fourth round.
The Foxes will host fellow Premier League side Brighton & Hove Albion in the next round.
Championship side Brentford took the lead in the seventh minute from a set piece, when the ball took two deflections, before Danish centre back Mads Bech Sorensen stabbed home his first goal in English football from close range.
Leicester started the second half on the front foot and equalised in the 46th minute, after Maddison found Cengiz Under in space for the Turkish winger to curl his effort past goalkeeper Luke Daniels.
Five minutes later, the visitors took the lead with a penalty, after Youri Tielemans was fouled. The Belgium midfielder got up to send Daniels the wrong way with a low shot into the bottom corner.
Leicester wrapped up the win in the 71st minute on the counter-attack, when Daniels spilled a Harvey Barnes shot and midfielder Maddison was on hand to score his fourth goal in as many games in all competitions.
Chelsea 3 Luton Town 1
Chelsea striker Tammy Abraham has grabbed a hat-trick against second-tier Luton Town to book the Premier League side's place in the FA Cup fifth round away to Barnsley.
Chelsea took the lead in the 11th minute, when a quick throw-in caught Luton's defence napping, allowing Timo Werner to make a run down the right channel and cut the ball back for Abraham, who fired a low shot past goalkeeper Simon Sluga.
Abraham doubled the lead six minutes later, when he flicked a header from Reece James' cross past Sluga, whose indecisiveness after coming off the line saw him stranded in no-man's land, as the ball sailed over him into the net.
Luton pulled one back on the half-hour mark, when Chelsea keeper Kepa Arrizabalaga failed to keep out Jordan Clark's low effort, which squeezed between his hand and leg into the net.
But Chelsea began to dominate in the second half and the introduction of Callum Hudson-Odoi had an instant impact, as his one-two with Billy Gilmour allowed him to fire the ball into the six-yard box for Abraham to get his third with a simple tap-in.
Werner had the chance to make it 4-1 with a penalty, after he was fouled by Clark, but the German, who has scored one goal in his last 15 appearances, saw his shot well saved by Sluga.
Chelsea's next opponents Barnsley beat fellow Championship (second-tier) side Norwich City 1-0 on Saturday.
Burnley 3 Fulham 0
Days after upsetting Premier League champions Liverpool at home, Burnley have continued their purple patch over Fulham.
All Whites striker Chris Wood was an unused reserve, as Jay Rodriguez scored a goal double.
They will host either second-tier Bournemouth or League Two Crawley Town at the next stage.