Gabriel Jesus stroked home with aplomb to put City in front after a free-flowing start before the visitors doubled their lead from a controversial penalty. Mullery was fuming after a disallowed goal and then being denied an equaliser when Brian Horton scored from the spot, only for referee Ron Challis to order a retake even though it was Palace players who had encroached into the box.Horton, inevitably, missed.
Christian Eriksen reduced the arrears in fortunate circumstances, his initial shot blocked by Aymeric Laporte before deflecting back off the Dane and past the stranded Ederson, with Sterling adding the third in the second half.
Chelsea's Olivier Giroud has now scored 19 Premier League goals as a substitute after netting two in eight minutes when he came on against Southampton.
"For the first time, we might be looking in the next couple of weeks at having a squad which gives me options to change people, options to bring people on in the later stages of the game, and changes in formation".
Zaha is Palace's talisman and has been a key player for the Eagles so far this season.More news: Three Kenya election board commissioners resign
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Roy Hodgson's team were in full control of the match, and a second goal arrived just before the quarter-hour mark when Tomkins forced the ball into the bottom corner from 10 yards after Brighton had initially made two blocks from goalbound efforts.
Huddersfield is a point above Palace after Tom Ince's stoppage-time goal sealed a 1-0 victory over Watford. Southampton's defeat earlier in the day mean Chris Hughton's side remain seven points clear of the bottom three and the cushion to the relegation places may well prove enough for both these sides. Brighton were beaten at Everton and at home to Leicester before being held by Huddersfield in a 1-1 draw last week.
Murray was particularly prolific during a run of results culminating in victory over Arsenal at the start of last month which saw Hughton named manager of the month and that appeared to have guaranteed Brighton's Premier League status for another season.
The Clarets were soon two ahead as Kevin Long notched his first-ever league goal for the club, rising to convert Johann Berg Gudmundsson's deep corner.
Jeffrey Schlupp is also closing in on a return to action as Palace brace for a decisive final five fixtures.