“I just tried to shoot it in, and it went in,” Ibrahimovic said to Viasat television after the match.
The French side were unbeaten in their eight previous matches and they had created the match's most clear-cut chances until Ibrahimovic rifled home the winner in the 64th minute.
After holding Milan scoreless in the first half, the hosts continued to hustle their illustrious opponents in the second half, with Delvin N'Dinga firing over from distance, before Milan delivered a hammer blow with their first shot on target of the match.
Seedorf's ball towards Robinho down the inside-right channel was cut out by the sliding Dudka, but Ibrahimovic seized on the loose ball to slam an unstoppable shot into the top-right corner.
It was the Swede's 11th Milan goal following his summer move from Barcelona
And Ronaldinho's late strike made sure there was no way back for Jean Fernandez's dogged but ultimately disappointed Auxerre.
Ronaldinho, a late substitute, put the game beyond Auxerre in injury time when he drifted in from the right wing before curling a precise shot into the bottom-left corner with his left foot.
"Ronaldinho made a good entrance. He played well and scored a great goal," said Milan coach Massimiliano Allegri.
"We were under heavy pressure at the start of the match and we felt a little bit trapped inside our penalty area, but everything finished well."
Victory gives Milan eight points from their five group matches, putting them beyond the reach of both Auxerre and Ajax, who will now compete for the consolation prize of a Europa League berth.
Milan, seven-time champions, host Ajax in their final group game, with Auxerre needing to better the Dutch side's result when they visit Real Madrid.
Brimming with confidence, Ibrahimovic expressed optimism for Milan’s side in the Champions League knockout phase.
“It’s too early to say, but whoever we meet, we’re going to win,” he told Sky Italia television.
Auxerre picked up their first points of the group phase by beating Ajax 2-1 in their previous outing and they started in purposeful fashion, with visiting goalkeeper Christian Abbiati called into action on several occasions.
The Italian caught an early header from Roy Contout before being tested by free-kicks from Darisuz Dudka and Valter Birsa.
Massimo Ambrosini was fortunate to avoid punishment for a two-footed lunge on Frederic Sammaritano, while Auxerre felt they should have had a penalty after Ignazio Abate and Alessandro Nesta both appeared to handle in the area.
Milan's best chance of the first half saw Clarence Seedorf send a half-volley whistle narrowly over from wide on the right.
Gennaro Gattuso also procured a sight of Olivier Sorin's goal but he side-footed wide shortly before the break.