A week after being United's Wembley hero in the EFL Cup, Ibrahimovic was centre-stage for the wrong reasons against 10-man Bournemouth.
The 26-goal Swede was lucky to escape without punishment after a retaliatory elbow on Bournemouth's Tyrone Mings – who had earlier trod on the striker's ear - and then saw a second-half spot-kick saved by Artur Boruc after Adam Smith had handled.
United, who stay in sixth place despite a 17-game unbeaten run in the Premier League, led the shots count 11-0 after 30 minutes but had to settle for a damaging draw when Josh King's penalty cancelled out the opening goal from Marcos Rojo.
The Argentinian scored his first goal for more than two years when he turned in Antonio Valencia's cross after 23 minutes. But in a rare attack, the visitors levelled when Phil Jones fouled Marc Pugh and King thumped in the spot-kick.
Andrew Surman was then sent off on the stroke of half-time when he pushed Ibrahimovic in the aftermath of the Swede's incident with Mings.
With 19 minutes to go in came United's golden chance. Pogba won United a penalty when his acrobatic reach to get Valencia's cross deflected off the arm of Smith.
Zlatan stepped up and struck his penalty well but Boruc did brilliantly to dive to his left and keep it out to earn Bournemouth a deserved draw at Old Trafford with the hosts failing to grab a top four spot.