Sulley Muntari was Milan's hero as he struck a 77th-minute equaliser to snatch a point for Massimiliano Allegri's struggling side at San Siro.
Mattia Destro had opened the scoring for the visitors early in the first half, but Cristian Zapata levelled just before the break.
Kevin Strootman looked to have sealed the points for Roma with a penalty early in the second period, only for Muntari's late strike to earn the hosts a share of the spoils.
The Ghana international's intervention means Rudi Garcia's men are now five points adrift of champions Juve, while Milan move into the top half of the table.
Allegri made four changes from Milan's 2-2 draw at Livorno, with Christian Abbiati, Mattia De Sciglio, Daniele Bonera and Muntari all returning to the starting line-up.
Despite Roma's dominance, Milan were level just before the half-hour mark through the unlikely source of Zapata.
Moments later, Roma thought they had gone back in front through Bradley, but the American's hooked volley bounced on the goal line and spun away to allow Milan to clear to safety.
Gervinho was released behind the Milan defence, only for the Brazilian to bring him down in the left-edge of the area.
After Bradley had missed another chance to extend Roma's lead, the hosts drew level again once more through Muntari on 77 minutes.
Mario Balotelli had two chances to complete an unlikely turnaround for Milan in the closing minutes as he first saw a vicious 20-yard free-kick parried away by De Sanctis, before then dragging a left-footed shot wide of the post from inside the area in injury time.
However, Allegri's team almost conceded with the last kick of the game, when Gervinho shot wide after smartly working an opening for himself.
