David Moyes’ side climbed to fifth in the Premier League – two points behind Chelsea, who beat Everton 2-0 earlier on Monday – and have a game in hand on their London rivals.
Jesse Lingard sparked West Ham into life at London Stadium when his menacing run into the penalty area drew a foul from Luke Ayling. Lingard, on loan from Manchester United, converted the rebound after his spot-kick was saved by Illan Meslier.
Leeds had found the net twice in a blistering opening spell, but Tyler Roberts’ finish was ruled out for a marginal offside against Helder Costa, and Raphinha ran the ball out of play before crossing to Patrick Bamford.
But they were two goals down before half-time when the unmarked Craig Dawson headed in Aaron Cresswell’s corner.
Marcelo Bielsa’s Leeds went close to a response five minutes after the restart when Raphinha’s sensational overhead attempt was tipped over by Lukasz Fabianski, while Bamford blazed over from Raphinha’s cut-back and Dawson cleared off the line as Leeds chased a late lifeline.
Pablo Fornals struck the crossbar for the hosts with a dipping second-half shot, but the Hammers ultimately held firm at the back to see out the three points.
“I’m disappointed with the performance,” England international Rice told Sky Sports. “We won but Leeds caused us a problems. Now we are starting to learn how to win ugly.
“This is the best squad I have been a part of. You look forward to training and seeing the lads and that shows on the pitch. We are fighting for each other. It is real special place to be at the moment. The place has a real buzz about it.
“It is hard to say we are going to be [in the] Champions League – there are so many games left. It will be a real tough test, but look where we are now and it is a massive upgrade. It is in our hands. If we want to believe we can be a European team we need to win the big games”.
Rice and Soucek at heart of West Ham efforts
Moyes said on Sunday that he would not sell Rice for £100m, which was reported to be the club’s valuation.
This match was the latest reminder of why Moyes is keen to ward off potential suitors as Rice, alongside the equally dependable Tomas Soucek, proved the antidote to Leeds’ incessant pressing, particularly in a second half which the visitors dominated for large periods.
In 22-year-old Rice and £19m summer signing Soucek, former Everton and Manchester United boss Moyes has a holding midfield combination he can trust, allowing West Ham’s attacking players to flourish.
Such solid foundations enable Lingard to shine. This was his fourth goal in six league appearances since his January move – as many as he had managed in his previous 38 in the competition for United.
Dawson, on loan from Watford, continues to prove as shrewd a signing as any. This was his 11th successive league start at the heart of West Ham’s defence and his fourth goal in all competitions this term.
Moyes claimed the experienced centre-back was “worthy” of a permanent deal after a match in which Dawson was involved at both ends, having hit a post with another header before half-time and somehow prevented Rodrigo’s shot creeping over the line in the closing stages.