Chelsea missed the chance to climb into third place while Brighton & Hove Albion edged a step closer to safety after a goalless draw at Stamford Bridge.
In an even first half, Chelsea's best opportunity fell to Kai Havertz but his close-range shot was saved by Robert Sanchez.
At the other end, Yves Bissouma's deflected effort looped onto the roof of the net.
It was Brighton who came closest to a winner in the second half as Danny Welbeck's shot from 20 yards came back off a post.
The visitors were reduced to 10 men in stoppage time as Ben White was shown a second yellow card, but their hosts were unable to capitalise in the seconds that remained.
Chelsea move up to fourth on 55 points, ahead of West Ham United on goal difference, but remain behind a Leicester City side who have a match in hand.
Brighton stay 16th but are now seven points above the relegation zone, with 34 points.
See: Chelsea report | Brighton report
Next fixtures
Chelsea: 24 Apr v West Ham (A)
Brighton: 24 Apr v Sheff Utd (A)
Match officials
Referee: Stuart Attwell. Assistants: Simon Bennett, Eddie Smart. Fourth official: Graham Scott. VAR: Kevin Friend. Assistant VAR: Darren Cann.
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