Liverpool led through James Milner's 27th-minute penalty, awarded after Paul Pogba inexplicably handled a corner as he went up to challenge Dejan Lovren.

Goalkeeper Simon Mignolet was Liverpool's hero with superb first-half saves from Ibrahimovic's free-kick and Henrikh Mkhitaryan, as Jurgen Klopp's side put up stern resistance and threatened on the break.

It looked like the visitors were going to hold on and move back to second in the Premier League, but United finally forced the goal they merited when Antonio Valencia reacted first when substitute Marouane Fellaini's header came back off the post, crossing for Ibrahimovic to head home off the bar.

Liverpool are now in third place, seven points adrift of top-flight leaders Chelsea, while United - whose nine-match winning run in all competitions came to an end - are now 12 points off the top.