The teenage forward was brought into the side in place of Ibrahimovic, who tested positive for coronavirus ahead of Thursday's one-legged tie at San Siro.
Milan was given a scare as Kasper Junker fired the Norwegian visitors ahead after 15 minutes but it took just 106 seconds for Hakan Calhanoglu to equalise from long range.
Colombo put Milan in front and Calhanoglu appeared to give the host breathing space, only for Jens Hauge to pull another back, but the Italian giant held on to set up a play-off with Rio Ave.
Bodo/Glimt entered the game unbeaten in 20 matches and took the lead through Junker's crisp finish from eight yards following some good play from Hauge out wide.
Calhanoglu promptly hit back for the home side with a powerful drive from range after being allowed to spin and drive forward 30 yards from goal.
A moment to remember followed for Colombo as the academy product rounded off a flowing team move after Calhanoglu flicked the ball into his path at the back post.
Not content with a goal and an assist, Calhanoglu smashed in a third for Milan with a low volley from outside the box at the end of a well-worked corner routine.
Hauge beat Gianluigi Donnarumma from 25 yards with a stunning effort to give Bodo/Glimt hope and Kjetil Knutsen's charges nearly took the game to extra time late on.
After Milan substitute Rade Krunic was denied by covering defender Brede Moe on the line, Ulrik Saltnes flashed a shot over from a good position at the other end in one final scare for the hosts.