The 39-year-old tapped in to open the scoring after Samir Handanovic saved his penalty and made it two moments later from Rafael Leao’s smart cross.
Romelu Lukaku pulled one back for Inter before the half-hour mark and was denied a penalty in the second half.
AC Milan held on to make it four wins from four and stay top of the table.
Some 1,000 fans were allowed inside the San Siro as Ibrahimovic made his return to the AC Milan side after a period of isolation following his positive Covid-19 test.
The former Sweden forward immediately picked up where he left off in September, taking his tally to four goals in two Serie A games.
He won a penalty after 13 minutes and was alert to finish on the rebound after Handanovic saved his first attempt, steering in a second soon after.
Inter forward Lukaku then turned home Ivan Perisic’s low delivery and almost levelled before the break when his header dropped narrowly wide from a corner.
The Belgian also saw a penalty decision overruled by the video assistant referee after he was seemingly brought down by goalkeeper Gianluigi Donnarumma.
Lukaku’s first-half strike was the first goal AC Milan have conceded in the league this season and they continue to be Italy’s form team, despite not having won a major trophy since 2011.
Stefano Pioli’s side are now unbeaten in 20 games in all competitions, having finished last season with nine wins and three draws in their final 12 matches.
Afterwards, all eyes where on Ibra, who was unplayable today. The Swedish forward has made a huge difference since arriving in January, and not even an enforced lay-off over the international break due to his positive Covid-19 test appears to be slowing the 39-year-old down.
“I lost my sense of taste a little, but I didn’t have any other symptoms,” Zlatan told Sky Sport after the match when asked about his brush with the virus.
“I swabbed myself every three days and I told myself that I would play in the derby whatever the cost, even if I were still positive!
“Better with age? Yes, I feel more complete and the experience helps. If I had the condition of a kid today, no one would stop me.”
Milan and Zlatan kick off their Europa League campaign on Thursday with a visit to Parkhead to take on Celtic.