Despite leading for the majority of the game, Jurgen Klopp's side conceded late on to a Diego Llorente header which leaves them two points adrift of the top four.
The result came after the seismic announcement of the new European Super League, in which the Reds will be a founding member.
Chelsea had double reason to celebrate on Saturday, as they not only moved into the FA Cup final thanks to a 1-0 win over Manchester City, but also enjoyed a boost in their top-four aspirations in the Premier League.
Despite being 2-0 down and reduced to 10 men thanks to a first-half red card for Craig Dawson, West Ham clawed the game back to 2-2 only to lose out late on.
David Moyes’ men have now played 32 games, one more than Chelsea, who are just a point back from them.
Indeed, for Steve Bruce’s side, the victory will go a long way to guaranteeing their survival, which had looked perilous until successive wins. Their tally of 35 points is eight more than Fulham in 18th.
Meanwhile, Sheffield United became the first team to be relegated from the Premier League on the day that Norwich’s promotion was confirmed from the Championship. The Blades have had a wretched season and sit on just 14 points.
Their latest loss came at the hands of Wolves, who have leapt into a mid-table position.
Due to the FA Cup semi-finals, there was a reduced calendar this weekend.
With Man City not playing in the Premier League this weekend, their lead at the top of the table was reduced to eight points, though they had played their game in hand previously so they and Man Utd have both played 32 fixtures.
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