The club, bottom of the table and under the temporary guidance of Mark Bowen, took the lead in the 52nd minute when Jamie Mackie scored.
But Jonny Evans and Darren Fletcher were both on target with headers from Wayne Rooney corners, before Anderson set up Javier Hernandez for a cool finish to settle matters.
Victory took United back to the top of the Premier League standings ahead of Manchester City's trip to Chelsea.
West Brom earlier moved up to third spot after a Simon Mignolet howler in the lunchtime kick-off helped the Baggies beat Sunderland 4-2 at the Stadium of Light.
The Black Cats goalkeeper gifted Shane Long the simplest of opportunities to fire into an empty net after they were already leading through Zoltan Gera's superb strike.
In the other afternoon matches, Jordi Gomez's hat-trick spared Wigan goalkeeper Ali Al Habsi's blushes as they overcame Reading 3-2, Everton and Norwich drew 1-1 and Stoke edged Fulham 1-0.