It was a half of very few opportunities, with Wayne Rooney having a decent opportunity before Paul Pogba drew first blood right before the break.
The second half burst into life, with James McArthur's equaliser and Juan Mata's disallowed goal, but it was Ibrahimovic who had the final say with his 88th minute winner.
Half of few chances
Jose Mourinho's side headed into this clash looking to build upon Sunday's 1-0 win over Tottenham, and they were the better side in what was a quiet first period.
The first real opportunity of the match didn't arrive until the 37th minute, it was an excellent reverse pass from Pogba which fell perfectly for Rooney. He lashed the volley towards goal, but Wayne Hennessey did well to deny him the opportunity to equal Sir Bobby Charlton's goalscoring record.
Pogba decided to have his opportunity in the 42nd minute, after picking Michael Carrick's floated ball over the defence but Hennessey was there once again.
In controversial circumstances
It didn't look like United would be rewarded for their efforts before the break, but managed to draw first blood in controversial circumstances right at the death.
A free-kick into the box looked to be flicked on by Ibrahimovic, which was easy for Pogba to slot home from six yards. Replays show it looks like it came off the arm of Ibrahimovic, and Pogba was offside but the goal stood.
Alan Pardew's side burst into life at the start of the second period, and their attacks on David De Gea's goal was led by McArthur.
He had a great opportunity in the 62nd minute, when he decided to have a crack from outside the area. It looked destined for the top corner, but De Gea did well to get a hand to it to guide it away.
However it wasn't long before the midfielder got his opportunity to get the Eagles back in it. It was excellent play from Pardew's side, when Damien Delaney's back-heel caught out the United defence and it was easy enough for the Scotsman to slot home.
Controversy strikes again
A lot had been said about referee Craig Pawson with some controversial decisions in the first period, and that didn't stop in the second.
Marcos Rojo managed to get his head to a cross in, which looked to come off the arm of Delaney but the appeals were waved away. The ball was played back into the area and Mata looked to have slotted home, but the flag was up for offside which proved to be the wrong decision.
Right at the death
United kept pushing forward as they looked to avoid their fifth draw in six league games, and were awarded for their efforts with two minutes to play.
Pogba had been excellent throughout, and showed great strength to hold off Yohan Cabaye and put Ibrahimovic through on goal. The angle was against the Swede, but he did well to get it beyond Hennessey and off the post to send the away support into a frenzy.
United are now six points off the top four.