The Brazilian star opened the score line early in the first-half from the spot and doubled the lead before the break.
Kaka fired home in the second period to widen the gap and register his second hat-trick ever since joining the San Siro side.
Roland Juhasz pulled on back for the visitors but substitute Alberto Gilardino scored in the closing stages of the match to seal the victory.
Egypt captain Hassan played the whole game, missing a golden opportunity when he was two meters away from the goal line and collecting a yellow card for protesting.
Milan now have ten points in Group H and can't be toppled off the first two spots in the two coming matches.
They are five points clear off French side Lille, who held on to second spot despite conceding a late Nikolaos Liberopoulos goal and losing 1-0 to AEK Athens.
Kaka Strikes
Milan didn't gave the visitors much time to organize themselves, breaking the deadlock as early as the sixth minute from the spot.
Yoann Gourcuff darted inside the area only for Juhasz to clip him before Kaka thundered the resulted penalty into the top corner of the net.
The talented midfielder waited only 15 minutes before scoring again when he played a swift give-and-go with Cafu before lofting the ball home past the advancing keeper.
Kaka continued his fantastic run with a close-range shot in the 56th minute, curling an unstoppable finish from the edge of the area into the far corner.
Juhasz made up for his foul inside the box when he headed an inch-perfect corner past Dida whose try wasn't enough o block the ball.
Anderlecht pressed hard for the second goal and Hassan almost revived his side's hopes in the game when he stretched to meet a powerful ball inside the area but his touch went over the bar.
Gilardino made it four two minutes from time when he latched on to a long pass to blast a first-timer home.
In Athens, Liberopoulos arrowed a low shot home in the 74th minute to give his side the first victory in the campaign.
AEK now have four points in third place, one point ahead of rooted Anderlecht.