Cagliari defender Pisano sliced a Robinho cross into his own net under pressure from Antonio Nocerino after four minutes to put the Rossoneri ahead in a first half the Sardinians went on to dominate.
Champions Milan put on a better performance after the break with Ibrahimovic doubling their lead on the hour after combining with Robinho as mid-table Cagliari's challenge faded.
"The second half was better than the first, but it's important to get three points to end the year with. We'll see what happens now in tomorrow's games," he told Italy's Sky Sport channel.
"There's no problem with the president," he said. "He can talk as he likes. I try to do things for the good of Milan."
Robinho should have doubled Milan's advantage on 58 minutes but after picking up Ibrahimovic's astute pass and skipping past Agazzi, the Brazilian blasted the ball over the bar from a tight angle.
Two minutes later, the two combined to stunning effect as Ibrahimovic played a one-two with Robinho and used his 1.95-metre frame to toe-poke the ball ahead of Agazzi's lunging dive and into the bottom corner.
Siena and Fiorentina battled to a goalless draw in a lacklustre Tuscan derby as the sides' ended the year languishing in the lower half of Serie A.
Striker Emanuele Calaio came closest to scoring for Siena, meeting Franco Brienza's left-wing cross with a brave header that came crashing back off the bar on 28 minutes.
