Roma travelled to struggling Milan looking to close the gap on leaders Juventus to three points after they had opened up a six-point gap with an eighth consecutive win on Sunday.
But despite bossing Milan in almost every department, Roma had to settle for their fifth draw in six matches to remain second, five points behind.
Roma took a 2-1 lead on 51 minutes when Kevin Strootman scored from the penalty spot but Milan were handed a lifeline when Muntari made the best of Mario Balotelli's pass to beat Morgan De Sanctis on 77 minutes.
Roma's Ivorian striker Gervinho looked particularly lively in the opening period and after being sent clear by Dodo forced Christian Abbiati to save down low at his near post.
But it was from Strootman's run down the left that Roma opened their account, Destro sliding in unchallenged to slot the ball home on 13 minutes as Milan's defence went missing.
It was Milan's 114th anniversary, but there was little to celebrate with Massimiliano Allegri's side struggling for rhythm against a well-oiled Roma side and Gervinho's lightning runs.
In the first 20 minutes only Kaka's shot, which sailed wide of De Sanctis's far post, gave any glimmer of hope.
However Milan found the breakthrough from a corner, Zapata meeting Muntari's header with a bouncing header of his own to beat De Sanctis on the half hour.
Roma thought they had restored their lead a minute later but Michael Bradley's effort from a tight angle bounced off the goalline.
Destro threatened again just before half-time but Milan's blushes were saved by a timely tackle from Daniele Bonera.
Abbiati failed to appear for the second half and was replaced by Gabriel, who after seven minutes failed to stop Strootman's spot kick, awarded after the 'keeper had fouled Gervinho on the edge of the box.
Milan had several claims for a penalty waved away in the second half, most notably when Balotelli tumbled to the ground under pressure from Mehdi Benatia
Milan were looking sloppy, and when Gervinho launched a counter-attack it took a timely tackle from Urby Emanuelson to stop the Ivorian yards from goal following a nice one-two with Adem Ljajic.
Totti replaced destro in the 64th minute and not long after the Roma veteran was involved in the build-up which saw Bradley head just wide from six metres out following Maicon's weighted cross into the area.
Milan had not looked likely to score an equaliser, but Muntari made the best of Balotelli's lay-off to the right on the edge of the area to beat De Sanctis down low to the keeper's left.
The goal revived Milan and the hosts had further claims for a penalty waved away when De Sciglio's cross into the area was chested down by Nicolas Burdisso.
Milan won a free-kick moments later when Montolivo was upended and De Sanctis did well to punch out Balotelli's fierce drive from the edge of the area.
Balotelli had a chance to win it for Milan at the death but after turning his marker in the box his tame left-foot shot went wide of the target.