The in-form Brazilian playmaker capped his latest impressive display by curling in a 25-meter shot in the 75th minute, adding another long-distance strike to his repertoire of recent stunning goals.
"He's a joy to watch," Liverpool manager Brendan Rodgers said of the 22-year-old Coutinho, one of the league's best players in 2015. "He's a kid who has so much ahead of him. A sensational footballer, and now he's starting to add the goals to mirror that quality."
Captain Jordan Henderson whipped in a near-identical finish to put Liverpool ahead in the 11th and although Edin Dzeko equalized in the 25th after a slick move, City was sluggish in a match it needed to win to keep the pressure on Chelsea.
City stayed five points behind Chelsea but has played a game more than the leaders, who beat Tottenham 2-0 in the League Cup final on Sunday at Wembley Stadium.
"I think we never give up about the title," City manager Manuel Pellegrini said. "We must try to improve our play first."
Liverpool, which is unbeaten in the league since Dec. 14, climbed above Southampton to fifth and stayed two points behind Manchester United in the race for Champions League qualification.
City managed to recover last April from Coutinho's winning goal — that time in the 78th minute — to go on a winning run and pip Liverpool to the title. It will take another huge effort to overcome Chelsea, especially on this evidence.
Liverpool was expected to be drained from a grueling Europa League journey in midweek to Besiktas, where it lost on penalties. The squad only returned to Liverpool at 4.30 a.m. on Friday.
Yet, Brendan Rodgers' team looked fresher than a sluggish City. The hosts' pressing game was relentless and top City players like Yaya Toure and Samir Nasri struggled to keep possession.
"To prepare yourself for a game against the champions like that is no mean feat," Rodgers said. "To play and perform at that intensity, you have to admire that."
And in Coutinho, Liverpool had the best player on the pitch, continuing his great run of form from the start of the year. Goals from long distance are becoming his speciality, having done so against Bolton in the FA Cup and Southampton in the league in the past month.
"The little magician at the end came up with a wonderful goal," Liverpool midfielder Adam Lallana said. "With players like that, we'll go far."
Coutinho played a key role in Henderson's goal, nipping in front of Vincent Kompany to pounce on Pablo Zabaleta's weak, short pass. He played in Sterling, whose sideways ball was taken on by Henderson before the stand-in captain curled a shot home from outside the area.
Lallana wasted two great chances — and had a goal disallowed for a marginal offside — while Sterling also exposed City's weakness at centre back to breeze past Eliaquim Mangala and shoot across the face of goal.
City was fortunate to be level at halftime. Aguero, who hit the post early on, cut inside and slipped in a pass that Dzeko — starting for the third straight game — ran onto and shot first time low into the corner.
City was one-paced after the break, despite the importance of picking up three points, and Liverpool created all the chances.
Sterling miscued from in front of goal and another Lallana goal was ruled out for an earlier offside. Coutinho made no mistake, though, cutting inside past Samir Nasri and curling a shot beyond goalkeeper Joe Hart.
Aguero and David Silva had late chances for City, but an equalizer would have been harsh on Liverpool.
"It is a significant win for us," Rodgers said."Suggest a correction