Spectacular long-range strikes by midfielders Jordan Henderson and Philippe Coutinho earned Liverpool a 2-1 victory over Manchester City on Sunday that seriously compromised the Premier League champions' title defence.
After Henderson's fine 11th-minute opener had been cancelled out by Edin Dzeko at Anfield, Coutinho curled home in sumptuous fashion from 25 yards to enhance Liverpool's hopes of Champions League qualification.
City now lie five points behind leaders Chelsea, who have a game in hand due to their involvement in the League Cup final, and manager Manuel Pellegrini admitted that the odds were against his side retaining their title.
"It was a close game, but Liverpool won because they scored two beautiful goals," he said.
"It is three points less with one game less. Of course it is difficult to reach the top of the table if you lose three points.
"But we must keep going and try to return to our normal performance and see where it takes us."
Both teams had gone into the game on the back of European disappointments, but whereas City's display suggested their 2-1 Champions League loss to Barcelona had not been fully digested, Liverpool showed no ill-effects from their penalty shootout defeat at Besiktas in the Europa League.
Liverpool only returned from Istanbul in the early hours of Friday morning and manager Brendan Rodgers said their performance against City was testament to the dedication of his players.
"I have to take my hat off to the players," said the Northern Irishman, whose side are on an 11-game unbeaten streak in the league.
"To get back at half four in the early hours of Friday morning -- by the time they got to bed it was six, and they had to sleep all of Friday.
"We then did some light work yesterday (Saturday), but to come out and play like they did, they were relentless."
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Rodgers added: "They restricted a top team to just one shot on target and deserve all the praise they will get."
Rodgers made four changes to the team that had come unstuck in Istanbul, with Daniel Sturridge among those who dropped to the bench, and saw his side take the lead in the 11th minute.
Henderson gathered a pass from Raheem Sterling, shifted the ball inside City captain Vincent Kompany and then curled an exquisite shot into Joe Hart's top-left corner from outside the box.
But City reacted quickly and after Sergio Aguero had hit the post, they drew level in the 25th minute when Aguero set up strike partner Edin Dzeko to beat Simon Mignolet from 10 yards.
A frenetic first half gave way to a more circumspect second period, but Coutinho gave the hosts victory with 15 minutes to play when he wriggled inside from the left flank and arced a shot past Hart from 25 yards.
It was his second stunning goal in a week, following his early strike in last weekend's 2-0 win at Southampton, and echoed his winning goal from Liverpool's 3-2 win over City in last season's corresponding fixture.
Victory took Liverpool up to fifth place, two points behind Manchester United, who occupy the fourth and final Champions League berth, and three points below Arsenal, who climbed to third by beating Everton 2-0.
Olivier Giroud had been one of the villains of Arsenal's shock 3-1 loss at home to Monaco in the Champions League in mid-week, missing a succession of chances, but he atoned with the opening goal at the Emirates Stadium.
The France striker struck six minutes before half-time, steering Mesut Ozil's right-wing corner home with an adroit right-foot volley, and Tomas Rosicky sealed victory late on with a deflected shot.
"We were focused. It was a mentally determined performance," said Arsenal manager Arsene Wenger, whose side now trail City by four points.
"You could see we suffered on Wednesday night against Monaco and that was still in our mind, but we were patient. That got us a good chance and we got a good win today."