Jordan Henderson and the Brazilian both scored magnificent goals either side of Edin Dzeko's equaliser to move fifth and deal Manuel Pellegrini's side a huge blow in the title race
After a bright start, the Reds took the lead through a sensational Jordan Henderson goal, the midfielder cutting inside on the break - capitalising upon a Vincent Kompany error - to curl a powerful long-ranger well out of the reach of Joe Hart into the top corner.
Manuel Pellegrini's men got back into it through Edin Dzeko's equaliser in the 25th minute but Liverpool's dominance told as the second half wore on, Coutinho plundering the winner with an astonishing thunderbolt into the corner of the net from the left flank.
The result sees Liverpool move ahead of Southampton into fifth place, while City remain five points behind leaders Chelsea having played a game more.
Any disappointment quickly faded, though, as Henderson arrowed in a fine strike from the edge of the penalty area after 11 minutes. Coutinho was again involved as he robbed Kompany before combining with Raheem Sterling to get the ball to Henderson, the Liverpool captain giving Hart no chance with a powerful shot into the top-right corner.
City – who also made four changes following midweek European disappointment against Barcelona – responded strongly, Aguero sending a low drive against the post a minute after Henderson's opener.
The champions continued to press and a crisp passing move involving Yaya Toure, David Silva and Aguero saw Dzeko bring them level after 25 minutes. The striker collected a perfectly weighted reverse pass from his Argentine strike partner before firing past Simon Mignolet from 12 yards.
Lallana had a chance to restore Liverpool's lead before the break from a chipped Lazar Markovic pass but pulled his effort wide of Hart's goal.
Both sides wasted chances early in the second half as Aguero and Sterling failed to convert from inside the penalty area, while Lallana had a second effort ruled out by the assistant referee. Silva then spurned a promising position for City with an over-hit free kick.
That proved to be costly as Liverpool finally made their possession pay, Coutinho cutting in from the left, evading the challenge of Samir Nasri and Pablo Zabaleta to secure the win.
Aguero went agonisingly close to earning City a point with a low effort after 79 minutes but the visitors were unable to find a second goal and, after late misses at both ends by Daniel Sturridge and Silva, handed the advantage to Chelsea in the race for the title.