The England international opened the scores on the 14th min before adding the second 10 min later, while Eric Bailly's 66th minute own goal gave Liverpool the consolation despite keeping more procession.
Meanwhile, Chelsea returned to winning ways after two consecutive league losses to beat Crystal Palace 2-1 courtesy of Willian's effort and Martin Kelly's own goal in the first half. Other EPL results saw Everton beat Brighton 2-0, as Burnley hammered Westham 3-0, while Leicester thumped bottom side Westbrom 4-1 to push them closer to relegation.
Elsewhere, West Ham have launched an immediate inquiry after supporters invaded the pitch during Saturday's 3-0 home defeat by Burnley in the Premier League.
At least two fans went onto the pitch after Burnley took the lead - with one approaching United's Mark Noble. Another fan ran on with a corner flag shortly after Burnley scored their second, with further incursions after the visitors struck a late third.