An even 90 minutes produced a number of openings, but the winning goal did not arrive until the 86th minute, with Joao Felix's brilliant effort proving to be the difference between the two sides.
Marcus Rashford had the first opportunity of the match in the third minute when he worked his way into the Atletico box before firing towards goal, but Jan Oblak was down to make a smart save.
Anthony Martial then raced into the Atletico box moments later, but the Frenchman could only lift the ball over the crossbar, as Man United made a bright start to the contest, with Victor Lindelof also heading just wide from a corner.
Angel Correa had Atletico's first opportunity in the 15th minute after the ball broke kindly for the forward inside the Man United area, but he fired over David de Gea's crossbar.
Ten minutes later, Atletico had another chance when Marcos Llorente delivered a low cross towards Thomas Lemar, but the Frenchman could not make contact at the vital moment, before Lindelof made a last-ditch challenge during a scramble inside the Man United box.
There was a brawl in the latter stages of the first half in Oslo following a challenge from Scott McTominay on Oblak, but the referee quickly gained control of the situation, handing yellow cards to both players.
The final chance of the first period came to Man United, with Rashford finding Anthony Elanga with a brilliant pass, but the forward could only fire into the arms of Oblak.
Simeone had wholesale changes just before the hour, with Axel Witsel, Felix, Saul Niguez, Antoine Griezmann, Koke and Alvaro Morata among those to enter the field.
Atletico had a golden chance to take the lead in the 68th minute when Saul found himself free inside the Man United box, but he somehow missed the crossbar.
Moments later, Eriksen was introduced for his Man United debut, with the Denmark international entering the field alongside Donny van de Beek.
Eriksen's first involvement saw him deliver a brilliant pass towards Elanga, but the attacker could not make contract, but it was an indication of what the attacker will bring to the club.
Down the other end, De Gea had to keep out a strike from Rodrigo De Paul before Maguire flashed a header wide of Oblak's post, with the match still level heading towards the final 15 minutes of action.
Facundo Pellistri then had an opening for Man United in the 83rd minute, but the Uruguayan youngster fired his effort straight at Daniel Wass after a Rashford shot had broken for him.
Atletico made the breakthrough in the 86th minute, though, when Felix worked space outside the Man United box before brilliantly picking out the bottom corner.
Fred was then sent off for the Red Devils in the final stages, as the game ended in disappointment for the English giants.
Man United will be in action once again on Sunday afternoon against Rayo Vallecano, which will be the team's final friendly of the summer before beginning their 2022-23 Premier League campaign against Brighton & Hove Albion on August 7.
Atletico, meanwhile, will take on Cadiz and Juventus in their final two pre-season matches before starting their La Liga campaign away to Getafe on August 15.