Both teams went into the game unbeaten in all competitions this season, but a hat-trick from the Turkish forward ensured that the Ligue 1 side kept their record intact.
A push by Alessio Romagnoli on Yazici in the penalty area meant referee Bartosz Frankowski pointed to the penalty spot. The 23-year-old then stepped up and easily beat Gianluigi Donnarumma.
The second came just before the hour mark when Yazici tried his luck from distance with a low shot which bounced just in front of the Milan goalkeeper and into the right hand corner.
Moments later Lille got their third after a quick counter attack sent Jonathan David one-on-one with Romagnoli, though the forward played a quick pass to Yazici who side-footed home.
Milan could do little to thwart a rampant Lille side and Jonathan Bamba could have made it four in the closing stages but fired over.