In a poor first half, the visitors created the first opening when Juraj Kucka blasted his effort high and wide.
Despite long spells of possession for Milan, they struggled to make any meaningful chances. A rare opportunity came midway through the half as Zlatan Ibrahimovic's free kick cannoned off the wall and behind for a corner.
Boateng's goalbound drive was blocked after the break before the away side were reduced to 10 men when Jankovic picked up his second yellow card for a foul on Ignazio Abate.
The Rossoneri finally broke the deadlock with four minutes to play when Boateng was on hand to fire in at the back post from Urby Emanuelson's cross.