Wayne Rooney’s brilliant instinctive winner beat Swansea as Manchester United ended a run of seven games without a win.
The England striker flicked home Anthony Martial’s cross with 13 minutes to go to settle a close contest.
After a dour first half, Martial had headed United in front, before Gylfi Sigurdsson’s glancing effort set nerves on edge at Old Trafford.
Manchester United move up to fifth, two points behind Tottenham.
Swansea’s raid forward were rare, but they twice came close to a second equaliser in injury time as Ashley Williams brought a good save out of David de Gea before goalkeeper Lukasz Fabianski headed narrowly wide from a corner with almost the last touch of the game.
West Ham 2, Liverpool 0
Andy Carroll scored against his former club as West Ham leapfrogged Liverpool in the table thanks to a first league double over the Reds for 52 years.
Michail Antonio beat Nathaniel Clyne to Enner Valencia’s early cross to net the Premier League’s first goal of 2016.
Liverpool midfielder Emre Can was denied by the bar but Jurgen Klopp’s side were off the pace throughout.
Carroll, who cost Liverpool a club record £35m in 2011, sealed the points after meeting Mark Noble’s cross.
West Ham’s second straight win lifted them to fifth in the table, Liverpool dropping to eighth.
Relive the action from Upton Park as it happened, plus all the best pictures and social media