Sitting third just past the halfway point in the Allsvenskan, AIK are the form team in the Swedish top flight and showed it with some slick passing in the first period.
They took the lead early in the second half, and in some style.
Swedish youngster Robin Quaison did not seem to have much on, but he turned inside and unleashed an unstoppable curling strike from 20 yards that substitute Ben Amos had no chance of keeping out.
United, who had several bright spells in the match, persevered and got a deserved leveller thanks to Chilean Angelo Henriquez, who tapped in Wilfried Zaha's drilled cross, ending the Red Devils' tour on a positive note.
It was a bright opening to the game, with United fielding a strong side that included returning captain Nemanja Vidic.
Wide men Nani and Wilfried Zaha were the real danger, with Nani especially looking in good touch before leaving proceedings due to injury.
He created several half chances for Robin van Persie, who was celebrating his 30th birthday, but the Dutchman could not find a way past the impressive Kenny Stamatopoulos in the AIK goal.
Andres Lindegaard, who was the last line of United's defence in the first-half, also looked resolute, blocking well from AIK talisman Martin Kayongo-Mutumba.
Just after the break, it was the home side who took the lead thanks to a real wonderstrike from Quaison, completely taking Amos by surprise, before he had even touched the ball after coming on
David Moyes' men have been a little below-par in the pre-season matches thus far, with two wins from five matches, but they responded strongly, with Vidic heading down into the pitch and off the crossbar from Ryan Giggs' corner.
Giggs and substitute Henriquez were starting to find a little bit of space in between the AIK midfield and backline, and the former picked out Zaha, whose low cross on the right side of the penalty area was comfortably slotted home by Henriquez at the far post for the equaliser.
United finished the game in the ascendancy, with Van Persie, wasting a golden opportunity to seal victory late on when his free header went wide, but Moyes will be pleased with the overall display of his side.