The return of Francesco Totti after two months out was not enough for Rudi Garcia's still unbeaten Roma, who are on 38 points and three clear of third-placed Napoli. Massimiliano Allegri's Milan are 10th on 19 points.
Roma twice allowed Milan to hit on the counter-attack and come back from a goal down with Muntari levelling for good in the 77th minute after taking Mario Balotelli's pass and firing home at the near post.
Mattia Destro had put Roma 1-0 up with his second goal in as many games in the 13th minute, with Cristian Zapata equalising in the 29th when he met Muntari's flick on from a corner with a clumsy header onto his knee and past Morgan De Sanctis.
Kevin Strootman restored Roma's advantage from the penalty spot five minutes after the break.
While Roma dropped precious points, they will be looking to the clash at Juventus right after the mid-season break on January 5 to apply pressure on their title rivals, providing Atalanta do not spring any surprises next weekend.