West Ham are still breathing down the necks of the top four.
They are not going away in the race for Champions League qualification — and the sense of disappointment from David Moyes and his players about this below-par performance was another sign of just how far this team have come.
First-half goals from Jesse Lingard and Craig Dawson put West Ham in control after a shaky start, but Leeds wasted several good chances in the second half and Moyes admitted the hosts rode their luck as they moved up to fifth, two points off fourth-placed Chelsea.
"We were fortunate at times but a little unfortunate at others," said Moyes. "We were resilient but didn't play well. I think the biggest step is that the players are really disappointed with how they played, so that shows you the standards we have set most of the season. But that is a good sign that they are all on board with that and recognised it."
It felt like this was a game that West would have lost 12 months ago.
Leeds had early goals from Tyler Roberts and Patrick Bamford ruled out inside the first eight minutes, but after a slow start West Ham summoned the character, through the composure of Declan Rice, to settle themselves and take control of proceedings.
It was another encouraging sign in their Euro push during the run-in.
Craig Dawson was once again remarkable at the back, blocking almost everything which came his way and clearing a late effort off the line to preserve a clean sheet.
West Ham have a game in hand on the teams above them and face a potentially defining game against Manchester United at Old Trafford on Sunday.
Rice said West Ham is a "special place to be" after the game last night and their European fate is in their hands. The Hammers still have Chelsea, Leicester and Everton to play. They will need to play better than they did last night, but if they show similar character then they will be in the mix come the end of the season.
"Speaking honestly I'm disappointed with the performance," Rice told Sky Sports. "We've won and scored two goals, but if you compare the performance against Man City last week and Leeds: at Man City we were brave, took the ball, played well and had loads of chances — a real performance; and last night Leeds caused us problems. Two disallowed goals, as players on the pitch you need to wake up and get yourselves in the game.
"Now we're learning to win ugly. If it had been 2-0, where we're trying to push ourselves for the end of the season, that would have been tough to come back."
West Ham's mentality has pushed them to new heights this season, as has the arrival of Lingard on loan from United. The 28-year-old has added a new dimension in attack and taken the burden off Michail Antonio, Jarrod Bowen and Said Benrahma.
Lingard is unable to face his parent club on Sunday, so Moyes need the likes of Benrahma, who is yet to score since joining from Brentford, to step up.
"I think he has grown into the Premier League," Moyes said of the Algerian. "It is not easy for him because we are looking for so many things from him, but he did a lot of good things.
"He ran the ball out, he took the ball under pressure, but I didn't particularly think the forwards played as well as they should have. You need the forwards to play well. We didn't do that well enough."