Chelsea beat Tottenham 2-1 on Tuesday to leave Roberto De Zerbi's men in danger of relegation from the Premier League with one game left of the season.
Enzo Fernandez opened the scoring in the 18th minute, curling home from outside the box, and Andrey Santos doubled the home side's league midway through the second half.
Tottenham gave themselves hope in the 74th minute when Richarlison converted from close range after Pape Matar Sarr's backheel.
Spurs poured forward in search of an equaliser but could not find another goal.
The result gives renewed hope to West Ham, who are 18th in the table, two points behind Tottenham.
Spurs, who have not been relegated since 1977, face Everton in their final match on Sunday with a draw realistically good enough for survival given their superior goal difference.
"We have to give everything for the club, for the badge, for the fans," said Spurs midfielder James Maddison.
"It's a bit embarrassing that we're in this position."
The Hammers must beat Leeds to have any chance of extending their 14-year stay in the Premier League.
Burnley and Wolves have already been relegated.
Chelsea's win at Stamford Bridge was their first in the English top division since early March and lifts them to eighth in the table.
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