George Williams put Fulham ahead at Craven Cottage on the stroke of half-time. Adrian Popa levelled for Reading just after the hour but within three minutes Fulham led again through Williams.
Popa got Reading’s second equaliser to earn the point that took them above Middlesbrough, who have played two matches fewer.
Fulham go five points clear in fifth, the final play-off spot.
Fulham 24 Jan v Middlesbrough (A)
Reading 29 Jan v Wolves (H)