The Reds are in sixth spot in the table on 53 points, ahead of Spurs thanks to their far superior goal difference and one point behind Aston Villa with a game in hand as they seek to salvage a disappointing season.
The visitors had to battle hard for their victory, with West Ham taking the lead in stunning fashion in the 12th minute when Lucas Paqueta cut in from the left and played a one-two with Michail Antonio before firing home from the edge of the area.
That lead lasted only six minutes as Dutch striker Cody Gakpo received a pass in a central position, taking a touch before quickly unleashing a bouncing shot that evaded the dive of Lukasz Fabianski before nestling in the far corner.
It took a brilliant piece of defending by Virgil van Dijk to prevent West Ham going ahead again just before the break as he got a toe to a superb angled ball from Said Benrahma to prevent Antonio from scoring at the far post.
Liverpool dominated possession throughout but the Hammers were dangerous on the break, and they had a brilliant solo goal by Jarrod Bowen ruled out after a VAR review found him to be offside early in the second half.
After having a shot blocked a minute earlier, Matip got the winner in the 67th minute when he powered home a close-range header from Andy Robertson's corner.
West Ham had a late shout for a penalty turned down when the ball struck the arm of substitute Thiago Alcantara as he went in for a tackle, but the referee waved away their appeals and VAR did not come to their aid as Liverpool hung on for their third win in a row.
KLOPP HAPPY
Manager Juergen Klopp was pleased with both the result and the performance, but the German said that qualifying for the Champions League was still beyond his side.
"No, it's not in our hands, so why should I talk about that?" he told BT Sport. "We can only get three points as often as somehow possible, that would put pressure on others but they are all in a better position."
Hammers boss David Moyes was left frustrated by the decision not to award his team a penalty for the handball, and he strode to the centre circle to confront referee Chris Kavanagh at the final whistle.
"When a player lunges in the box, it's different from a slip, it's different from trying to break your fall. When you lunge in the box, your arms out, it was a penalty kick," he told BT Sport.
The loss brought an end to a run that saw West Ham take seven points from three games and dropped them one spot to 14th, five points ahead of Leicester City in 18th place.
