The game continued at an impressive tempo, but neither side could muster too much in front of goal, allowing Keisuke Honda to seek out an effort from range that was handled comfortably by Handanovic.
Jovetic sought to turn the screw for Inter just before the interval as he sized up an effort from 25 yards out, leaving a line of retreating Milan defenders to see the ball whistle just wide of the target.
The Nerazzurri should have taken the lead right on the stroke of half time, but Mauro Icardi was denied by Diego Lopez down low after the frontman had broken through from Ivan Perisic's defence-splitting ball.
Inter continued to press for an opener after the break when Perisic and Guarin combined, the latter midfielder's eventual header flying off target to spare Milan's blushes.
The breakthrough fell just a few moments later, however, this time as Guarin went on a stunning solo run before firing an unstoppable effort into the bottom corner of Lopez's net to make it 1-0.
Milan introduced Mario Balotelli as they went in search of a leveller, and the former Liverpool man combined well with Adriano, leaving Juraj Kucka to eventually turn an effort across the face of goal.
Icardi thought he had capped off the game for Inter as the minutes ticked by, but the frontman saw his header flash over the bar having made a good run to beat his marker at the near post.
Balotelli might have put his name in the headlines just before the close of the encounter, although his 25-yard screamer came back off the post after beating Inter stopper Handanovic.
The maverick forward kept up the pressure in the dying embers, and he forced another good save from the home goalkeeper with a low strike down towards the bottom corner.
AC applied yet more pressure as they went in search of a last-gasp equaliser, but Handanovic's saves were to prove vital as La Beneamata held on for all three points.