Paul Pogba had looked like being the villain of the piece for United, but Ibrahimovic's header – his 10th goal in 10 top-flight games – prevented a damaging defeat.
James Milner's 27th-minute penalty and sixth league goal of the season – awarded after a handball from Pogba – had looked like it would prove to be the winner at Old Trafford.
Pogba missed a brilliant opportunity to put United ahead prior to Milner's strike, while Simon Mignolet had made key saves from Ibrahimovic and Henrikh Mkhitaryan in the first half, but had barely been troubled prior to the veteran Swede's intervention.
United's nine-match winning streak in all competitions is now over, but they still sit within five points of second place after salvaging a draw.
Liverpool, meanwhile, are winless in four matches and trail leaders Chelsea by seven having dropped from second to third over the course of the weekend.
The hosts had threatened first when Ibrahimovic – one of four players brought into Jose Mourinho's team - charged down Mignolet after a weak back-pass from Dejan Lovren and watched the ball deflect agonisingly onto the roof of the net.
United then squandered a golden chance to take the lead when Mkhitaryan produced a superb throughball to release Pogba, but the midfielder could only drag his left-footed shot wide.
Pogba's first half got worse when Milner swept in a corner from the right and the France international's raised arm inside the area prevented Lovren from attempting a header.
Milner took the penalty himself and confidently beat David de Gea despite the goalkeeper correctly diving to his left.
Mignolet made a brilliant stop from Ibrahimovic's powerful 20-yard free-kick at the other end, saving the visitors after Divock Origi – starting as one of four Liverpool changes - had brought down Ander Herrera in a dangerous position.
The Liverpool keeper was alert again to keep out Mkhitaryan's left-footed strike after the playmaker had been fed by Herrera, ensuring Jurgen Klopp's men had a half-time lead.
Mourinho brought on Wayne Rooney for Michael Carrick at the break, the United captain's 450th Premier League appearance.
Origi saw an effort deflect narrowly wide, but the hosts were soon in the ascendancy when a fast counterattack – prompted by Anthony Martial dispossessing Trent Alexander-Arnold on his Premier League debut - led to Mkhitaryan's cut-back just evading the France forward.
Klopp then introduced Philippe Coutinho from the substitutes' bench and his change almost had an instant impact with the playmaker setting up compatriot Roberto Firmino, only for De Gea to make a two-handed stop.
Juan Mata, who had scored three goals in his last four league games against Liverpool, replaced Martial, but United were finding it more difficult to create openings, Rooney shooting wide from one rare chance.
If anything, the visitors were looking more likely to put the game beyond United, Adam Lallana denied by De Gea and Georginio WIjnaldum just off-target with a header.
But Ibrahimovic struck in dramatic fashion, his looping header from Antonio Valencia's cross beating Mignolet and a despairing clearance from Lovren, the move kept alive after substitute Marouane Fellaini had headed Rooney's delivery against the post.