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," said Pellegrini. "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.”
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 is on an 11-game unbeaten streak in the league. "We then did some light work yesterday [Saturday], but to come out and play like they did, they were relentless.”
Arsenal move to third as Giroud makes amends
Olivier Giroud made amends for his midweek nightmare against Monaco to set up Arsenal's 2-0 victory over Everton at the Emirates Stadium that moved Arsene Wenger's side back up to third in the Premier League on Sunday.
Giroud was guilty of missing a succession of chances in the 3-1 Champions League defeat but showed he had put the experience behind him when he volleyed his side's 31st minute opening goal with Tomas Rosicky wrapping up the win in the 88th minute.
Arsenal looked shaky at the start but soon made amends as Giroud — who was handed the chance to prove himself by Wenger — took full advantage of poor marking by Everton defender John Stones to put his side ahead in the 39th minute.
Everton had faded after a positive start during the first half but their approach to the second half suggested they remained confident of finding a way back into the game.
But any hopes of a comeback disappeared in the final moments of the game when Rosicky's shot was deflected past Howard off Phil Jagielka.
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