A first half penalty from Franck Kessie and a second half strike by Brahim Diaz were enough to ensure the Rossoneri returned north with all three points.
It was the hosts who were the better of the two teams in the opening quarter of an hour as they looked comfortable in possession, although they lacked the quality needed to unlock the Rossoneri’s backline.
With the slow start behind them it was Stefano Pioli’s men who would assert their dominance on the contest and Simon Kjaer came close to giving them the lead halfway through the opening 45 minutes, but his awkward looking header was kept out by the crossbar.
Despite seemingly being able to carve open the Rossoblu defence at will, the Rossoneri were struggling to find the finishing touch as they laboured in the final third and failed to create any clear cut opportunities.
However, with the half time whistle approaching Milan’s persistence paid off when they were handed the chance to take the lead from the penalty spot after Ante Rebic was brought down in the Crotone box. Kessie stepped up and calmly slotted the spot kick past Alex Cordaz to send the Rossoneri into the break with a deserved advantage.
The break did little to quell the visitor’s momentum and it took them less than five minutes of the second half to double their advantage when Hakan Calhanoglu’s long run was finished off by Diaz.
Then with the game approaching the hour mark the Rossoneri were dealt a blow when Rebic was forced from the field with a serious looking elbow injury, much to the displeasure of an incensed Pioli.
As the contest entered its final quarter it became a scrappy affair with neither team seeming able to offer much in the way of creativity as the middle of the park became the main battle ground.
The Rossoneri did have the chance to extend their lead just before the full time whistle, but Rade Krunic’s long range effort hit the bar and Milan were forced to settle for a comfortable, if not overly impressive, victory.