After being outplayed for large spells of the game, Milan eventually broke the deadlock against the run of play with less than 10 minutes remaining as Zapata's strike took a wicked deflection off the heels of Emilio Izaguirre, leaving Forster helpless as the ball trickled into the bottom corner.
The Serie A giants then doubled their lead moments later through Muntari, who bundled home from close range after Forster had pulled off an excellent save to palm away Mario Balotelli's free-kick.
Prior to the game, much was made of AC Milan head coach Massimiliano Allegri's lengthy injury-list which included the absence of Kaka and captain Riccardo Montolivo, and indeed they looked disjointed for most of the match.
The Hoops dominated possession for large spells of the first half, but found chances few-and-far between with Kris Commons and Charlie Mulgrew both guilty of wasting set-pieces in good positions, while Adam Matthews caused numerous problems down the right.
The hosts' best opportunity of the opening 45 minutes came just before the break as Balotelli's strike from distance required Fraser Forster to scramble across goal to tip wide after a wicked deflection by Efe Ambrose, before Muntari acrobatically fired over.
Neil Lennon's side looked to be on course for a point, although they did have chances to win the game with Giorgios Samaras firing wide in the early stages of the second-half and Anthony Stokes clipping the crossbar with a curling free-kick.
Muntari missed a glaring opportunity to take the lead when he headed over from close range on the hour mark as Milan became increasingly frustrated, while Celtic grew in confidence.
The home side were struggling against Neil Lennon's men and in need of some inspiration as the game entered the final stages.
However, they got a huge slice of luck when Zapata's drive in the 82nd minute appeared to be heading wide before it deflected off left-back Izaguirre and ended up behind Forster.
The Hoops goalkeeper was beaten again four minutes later despite making a great save from Balotelli's free-kick, as Muntari knocked in the rebound.
The two late goals, though, were a sickener for Celtic who take on Barcelona in their next group fixture at Parkhead at the start of October with Ajax also waiting in the wings.
However, on their overall display, they can go forward in the group with some confidence.