Ibrahimovic netted the first goal in the 64th minute before Ronaldinho added the second during injury-time.
The result guaranteed Milan second place in Group G as Ajax Amsterdam slumped to a 4-0 defeat against leaders Real Madrid.
Swede Ibrahimovic had previously crushed Auxerre in September's group opener when he scored two goals in three minutes to give Milan victory.
"That is what it is like to play against talented players. With half a chance, they sweep the ball home. They have Ibrahimovic up front who can make the difference anytime he wants", Auxerre midfielder Benoit Pedretti told French channel Canal plus.
"We did a good match, we gave our maximum, we keep learning, he added. We showed our limits, we tried to enjoy ourselves. There are no regrets to be had."
"We tried our hearts out. It was a difficult match, a difficult venue. We can relax a bit in the last game," Ibrahimovic told Sky.
"We will play our game and whoever we meet in the next round, we will win," he added.
The French club piled on early pressure on to Milan's defence, forcing goalkeeper Christian Abbiati to make several saves.
After the interval, both teams remained well organised and struggled to reach their opponents' penalty area until Ibrahimovic fired a powerful shot over goalkeeper Oliver Sorin and under the crossbar.
Milan's Ronaldinho came on as a substitute for the last five minutes, returning to the pitch where he started his career in Europe with Paris Saint Germain back in 2001.
"Definitely getting through gives us more strength. I think for us, it was an important night," Milan coach Massimiliano Allegri told Sky.
