United got off to the best start possible when Antonio Valencia released Jesse Lingard away on the right flank, Lingard then put in a first-time cross in for Ibrahimovic and the Swede headed it excellently to give his side the lead.
Wayne Rooney went very close to equalising Sir Bobby Charlton's record when his shot hit the post thanks to a great save by former United man Ben Foster.
Ibrahimovic sealed the three points early on in the second half, when he created a chance for himself inside the box with some good footwork, his resulting shot was deflected by Gareth McAuley into the corner of the West Brom net.
Let's take a look at the player ratings for Jose Mourinho's side.
At the back
David De Gea (8/10)
The Spaniard was rarely tested throughout the game as West Brom failed to get the delivery properly to their frontman Salomon Rondon and whatever came De Gea's way was comfortably handled by him.
Antonio Valencia (9/10)
Another excellent performance from the ever-dependable right back, set up Zlatan's goal when he released Lingard into space in the first half. He was able to get into the final third himself on a few occasions and trouble the West Brom defence.
Phil Jones (9/10)
Jones put in another commanding performance at the back alongside Marcos Rojo, dealt very well with the threat of Rondon and was rarely caught out in another stellar showing in defence.
Marcos Rojo (8/10)
Much like Jones, Rojo had an excellent game as well. Was involved in a nasty incident with Rondon, but this time the Argentinian didn't get himself into much trouble and put in a solid showing at centre-back.
Matteo Darmian (8/10)
Picked ahead of Daley Blind for this game, Darmian showed some good defensive work, but he was targeted repeatedly by the likes of Matty Phillips and Chris Brunt and also by some long balls that came his way, but the Italian stood firm and was also helped at times by the defensive work of his captain Wayne Rooney.
Michael Carrick (8/10)
It was yet another silent yet effective showing from the 35-year-old in the middle of the midfield for United, dictated the play from the back and was always looking for a forward pass when in possession.
Ander Herrera (8/10)
An energetic showing from the Spaniard as he had a tough day against the likes of Claudio Yacob and Darren Fletcher, he was all over the pitch linking with the likes of Lingard and Pogba, but failed to create much himself.
Paul Pogba (9/10)
Another dominant performance in midfield for Pogba against West Brom, Pogba dealt well with the physicality of Pulis' side and linked up well with the likes of Rooney, Lingard and Ibrahimovic in the final third. Although he did misplace a few of his passes, his overall contribution was excellent.
Jesse Lingard (9/10)
Lingard was a surprise starter for this one and produced a great performance to help his team to victory. He was a constant menace both off the ball and on it as well, assisting Zlatan's opener with an excellent delivery into the box and was full of energy down the wings for United.
Wayne Rooney (8/10)
Rooney put in a shift in the game, his defensive contributions were much more vital in the victory. He was unlucky to not get the all-important record goal for United when his shot was saved by his former teammate Foster. Saved Darmian with some very good defensive work deep in his own half.
Zlatan Ibrahimovic (9/10)
Ibrahimovic's performance throughout the game showed exactly why it is wrong to term the 35-year-old as 'finished'. Took the first goal early on excellently and was looking to link up more with Rooney in this game in the final third. He was involved in a rather unnecessary incident with Craig Dawson and was lucky to get away with a yellow card. He sealed the victory in the second half when his deflected shot went past Foster to give the Swede his 11th goal in the Premier League this season.
Marcus Rashford (8/10)
Rashford came off the bench once again late in the second half and threatened the West Brom defence with his blistering pace, was unlucky to not go clear on goal when he was taken down by the aggressive Brunt.
Marouane Fellaini (7/10)
Another appearance off the bench for the Belgian in this one as he replaced Rooney late on in the game, kept it simple and did not make any mistakes that the opposition could take advantage of.
Chris Smalling (N/A)
Came off the bench very late in the game and while he didn't have much time to do anything, his return will be a positive sight for United fans.