West Ham 2 - 0 Liverpool
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.