The London club moved above Cardiff City, whose promotion push suffered a blow when they lost 1-0 at fourth-placed Aston Villa after Jack Grealish volleyed an 85th-minute winner.
Fulham have 81 points from 42 games and are a point clear of Cardiff, who have a game in hand. Villa are four points further back.
Leaders Wolverhampton Wanderers, who are eight points clear of the chasing pack, host Derby County on Wednesday.
None of the bottom six teams won, with Sunderland missing a penalty and conceding a late equaliser in a 1-1 draw at home to mid-table Norwich City.
Ipswich Town won 1-0 at home to Barnsley before their manager Mick McCarthy announced he was leaving the club with immediate effect.
(Reporting by Toby Davis; Editing by Ken Ferris)
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