James Forrest opened the scoring after a one-two with Odsonne Edouard as Celtic comfortably secured their place in Friday’s draw 6-1 on aggregate.
That was Forrest’s seventh goal in his last eight games.
Sebastian Larsson then gave AIK a glimmer of hope from the penalty spot but a minute later Mikey Johnston had his low cross fumbled over the line by AIK keeper Oscar Linner.
Late goals from Christopher Jullien and Lewis Morgan rounded off a good night’s work by Neil Lennon’s side in the Solna Arena. Start forecasting your Weekend Games Now on NaijaBet
But Lennon was left worrying over the fitness of Kristoffer Ajer, who went off injured early to make him a major doubt for Sunday’s visit to Rangers.
Celtic’s arch rivals were in action later, hosting Legia Warsaw with part of their Ibrox ground closed as a punishment for racist behaviour of their fans earlier in the competition.
Celtic were not the only wide margin winners, with PSV Eindhoven progressing 7-0 on aggregate after a 4-0 win over Apollon in Cyprus.
But Northern Ireland’s Linfield were knocked out on away goals after a 2-1 loss at Qarabag left them tied 4-4 with the Azerbaijan side.
Other teams marching on to the competition proper were Spain’s Espanyol and FC Copenhagen.
Among the later kick-offs were Wolves, hosting Torino after a 3-2 first-leg win in Italy.
The English Premier League side are playing in their first European campaign since 1981.
Friday’s draw is at 12:00 in Monaco.