The visitors went into the game knowing they needed to win to keep their Champions League qualification hopes in their own hands but mid-table West Ham made the better start on Sunday.
Sam Byram saw an early chance narrowly miss the target before Edimilson Fernandes forced a good stop from away keeper Simon Mignolet.
Coutinho saw an effort fly narrowly over the crossbar on 26 minutes and Liverpool were ahead soon after as Jurgen Klopp’s men began to dominate.
Daniel Sturridge, making a rare start for the Reds, broke the deadlock after rounding Adrian having been picked out by Coutinho.
West Ham could – and probably should – have been level before the break as the ball fell to Andre Ayew from a corner but he could only find the post from two yards out, with the Ghanaian then hitting the upright again from the rebound under pressure from Sturridge.
Liverpool pressed for a second after the restart as Georgino Wijnaldum and Adam Lallana were both denied by Adrian but they didn’t have to wait too long to double their advantage.
Coutinho made space for himself on the edge of the area and fired home on 57 minutes, with the Brazilian grabbing a second soon after having skipped past a static Hammers defence before slotting the ball into the net.
Divock Origi made sure of the result with quarter of an hour to play as he reacted quickest after Adrian had failed to deal with a high ball into the box.
Liverpool move up to third as a result of their victory and will qualify for next season’s Champions League if they beat relegated Middlesbrough in the final round of fixtures next Sunday.
Southampton have announced plans for a two-week tour of China as part of their pre-season preparations for the 2018-19 season.