Giampaolo Pazzini scored a hat-trick on his AC Milan debut to earn the Rossoneri all three points from their trip to Bologna.
The former Inter Milan striker opened the scoring from the penalty spot in the 16th minute, but the Rossoblu responded well with Alessandro Diamanti scoring a deserved equaliser from the spot on 42 minutes.
But Pazzini wrapped up victory with two goals in eight minutes towards the end of the match at the Stadio Renato Dall'Ara.
The game kicked off only moments after a heavy downpour had dumped copious amounts of water on the pitch and both teams seemed a bit stuck in the mud for the first five minutes.
Milan came to life first with Kevin-Prince Boateng twice testing Federico Agliardi with free-kicks, hoping the ball would skid off the surface, but Bologna's goalkeeper was not caught out on either occasion.
The first penalty of the game was awarded in the 16th minute when Nicolo Cherubin tugged on the shirt of Pazzini, who duly tumbled inside the area.
Pazzini stepped up to the spot to open his account for the Rossoneri.
Inspired by Italy international Diamanti, Bologna searched for a way back into the game, but Saphir Taider squandered it in the 31st minute when he had a clear sight of goal, instead shooting over the crossbar from 10 yards out.
Five minutes later, Diamanti's low cross flashed just past Robert Acquafresca, who lunged in front of the Milan goal.
Bologna then levelled through the second penalty of the game, and it was no surprise that Diamanti earned it as he was fouled by Antonio Nocerino just inside the penalty area.
And Diamanti stepped up to send Christian Abbiati the wrong way and bring Bologna level in the 42nd minute.
Tiberio Guarante dragged a shot wide of the far post in the 48th minute as Bologna carried forward the momentum from the first half into the second.
It did not last long, though, as both sides tired rapidly.
Diamanti still caused some confusion in the Milan penalty area with a dangerous curling free-kick, but it was Milan who regained the lead with Agliardi gifting a second goal to Pazzini.
The Bologna goalkeeper was disturbed by his own player as he went to claim Luca Antonini's deflected cross, but the ball fell for Pazzini, who swept it in from two yards.
Pazzini then completed his hat-trick in the 85th minute, cleverly guiding Nocerino's shot into the bottom corner with his back to goal to seal victory for Massimiliano Allegri's men.