James Milner put the visitors ahead with a 27th minute penalty after the world's most expensive player, Paul Pogba handled the ball in the box, before Ibrahimovic scored his 14th league goal in his debut season.
The result leaves Liverpool who had goal keeper Simon Mignolet pull great saves third on the log, while united remain sixth just four points adrift top four position.
Elsewhere, Everton produced a brilliant performance to beat Manchester City, 4-0 with Romelu Lukaku, Kevin Miralas, youngster Davies and new signing Lookman on target.
The result leaves City fifth on the table 10 points off leaders Chelsea.
On Saturday, Chelsea yesterday extended their lead at the top of the English Premier League with a three nil win over Leicester.
A brace from Marcos Alonso and additional goal from Pedro Rodriquez gave the Blues the comfortable win. Elsewhere, Arsenal bounced back to winning ways in the league after thrashing Swansea four nil at Liberty Stadium, while Harry Kane scored a hat trick as his side beat West Brom four nil.