Milan eased into a comfortable two-goal lead at the break thanks to goals from Ante Rebic in the eighth minute -- a goal that was brilliantly set up by Ibrahimovic -- and a fine Franck Kessie finish on the stroke of half-time.
Milan's task became much more difficult just before the hour mark, however, as out of the blue, Ibrahimovic was given a straight red card for something he said to the referee, much to the Sweden international's bemusement.
AC Milan coach Stefano Pioli said that Ibrahimovic informed him that he did not disrespect or offend the referee.
"I just talked to Zlatan, he told me that he argued with the referee and it lasted some time," Pioli told Sky Sport Italia. "He assured me that he did not disrespect him and above all he did not offend.
"What did he report to the referee? Zlatan said to me that he said 'you really don't care what I tell you'."
The 39-year-old's Swede's eighth red card in Europe's top-five leagues, and first in Serie A since February 2012, was a strange one, given the referee and Ibrahimovic were not close to each other when the Milan striker was dismissed.
Riccardo Gagliolo got Parma back into the match six minutes after Ibrahimovic's red, but Rafael Leao added a late third for second-placed Milan as Stefano Pioli's men closed the gap to Inter Milan to eight points, with the league leaders facing Cagliari on Sunday.
Parma remain in trouble down in 19th in the standings, four points from the safety zone.
Pioli pointed out that his main goal was to get his side back into the Champions League after a seven-year absence, with Milan moving seven points clear of fifth-placed Napoli in what is a tightly-contested top-four race.
"I liked the approach seen by the boys after the match against Sampdoria [in last weekend's draw]," Pioli added. "We needed a reaction.
"We almost messed up the match in the second half but it was important to win and get closer to the Champions League.
"We had to show that we understood our mistakes and put in a different performance. We were faster and we found more solutions."