In our best away performance of the season, Zlatan put the Reds ahead inside five minutes and the visitors then controlled the match from the first minute to the last for a fourth successive win.
United stay sixth, level on points with Spurs, but are now only four points adrift of second-placed Arsenal, with two home matches against Sunderland and Middlesbrough to come over Christmas.
The Reds started brightly from the off and moved ahead with our first attack of the game.
After superb build-up down the right, Antonio Valencia found Jesse Lingard and he in turn picked out Zlatan with a superb cross and the Swede headed home from close range.
The Baggies threat, predictably, came from their set-pieces and one such moment provided their best chance of the game.
Jonas Olsson met Chris Brunt's flag-kick but his header across goal evaded his onrushing tea-mates and the ball drifted harmlessly wide.
Wayne Rooney then came with inches of equalling Sir Bobby's record when Ben Foster tipped his piledriver on to the bar after lovely link-up that involved Lingard and the again impressive Paul Pogba.
West Brom slowly worked their way back into the game and went close twice before the interval through Brunt - who fired straight at David De Gea - and Matt Phillips, who lashed narrowly off target.
It was United who should have scored again before the break however as Lingard blazed over the bar from close range when well-placed.
The Reds started the second half as we had the first and soon deservedly doubled their lead.
Pogba tried to catch out Ben Foster with an impudent lob, but the former United keeper was left with no chance from our next attack.
Ibrahimovic exchanged passes with Rooney, cut inside two defenders and his shot took a deflection of Craig Dawson to wrong-foot Foster for his tenth goal in as many games.
Marcos Rojo and Salomon Rondon were then both booked after a fiery coming together, with the West Brom man perhaps fortunate not to see red after he hit out at the Argentinian.
Pogba forced a save from Foster from distance and then clubbed an effort over the bar, but there was no further action as United kept Tony Pulis' side at arms length.
Chris Smalling made his return from injury deep into stoppage time as the Reds cruised to a fourth successive win with the frantic festive fixtures on the horizon.
Overall team performance: 9/10
United Faithful Man of the Match: Zlatan Ibrahimovic. Six foot five.