The Premier League champions are still 11 days away from the start of their title defence and were made to look mediocre at times by opponents who are flying high in their domestic league midway through their season.
Missing Wayne Rooney, who is at the centre of ongoing transfer speculation but was left out due to a shoulder injury, David Moyes’ side needed two good saves from Anders Lindegaard to deny Kennedy Igboananike and keep them on level terms in the first half.
AIK did take the lead shortly after the restart at the Friends Arena thanks to a superb strike by Robin Quaison, but United had Angelo Henriquez to thank for netting the goal that earned them a draw midway through the second period.
The Chilean converted a Wilfried Zaha assist to score his first senior goal for the club.
United face FA Cup holders Wigan Athletic in the Community Shield on Sunday before travelling to Swansea City in their opening league game on August 17.