Mirko Vucinic put mid-table Roma ahead midway through the first half with his third goal in three games against Milan when he shrugged off Marek Jankulovski and blasted home.
Alexandre Pato equalised just after the restart when he tapped in Kaka's cross and the 19-year-old Brazilian soon clipped in a superb second.
Montenegro striker Vucinic again netted with a clever diving header on 72 minutes to bring the hosts level and both sides had decent chances to win the game in a frantic last few minutes.
Beckham, on loan from Los Angeles Galaxy for two months in a bid to stay in the England reckoning, was given a surprise start in Milan's three-man midfield and was tidy before being substituted on 89 minutes.
The 33-year-old had one shot and put in a few crosses but often dropped deep, playing as a defensive midfielder at times.
JUVE CUT GAP
Second-placed Juventus earlier cut the gap on Serie A leaders Inter Milan to four points after an Alessandro Del Piero free-kick gave them a 1-0 home win over Siena.
Champions Inter drew 1-1 at the San Siro with Cagliari on Saturday and are now nine points ahead of Milan in third.
Juve made sure they took advantage of Inter's slip despite looking rusty after the three-week midseason break.
Del Piero has lit up the Champions League this season with some memorable free-kicks and he produced another piece of magic just after the half hour mark when he found the bottom corner.
"We are doing well but it is clear Inter need to lose more ground. It is still a long road and we can do it," Del Piero told reporters.
The 34-year-old had a couple of other half-chances for Juve but they were forced to cling on at the end with goalkeeper Alex Manninger defying his former Siena team mates.
Napoli moved up to fourth after Christian Maggio's tap-in 10 minutes from time sealed a laboured 1-0 home win over Catania.
The visitors, who had a goal ruled out after the referee had already blown for halftime, appealed for offside but Maggio's goal stood and made up for Marek Hamsik's missed penalty.
Fiorentina are a point further back after losing 2-1 at home to Lecce, who climb out of the bottom three thanks to their first win in 13 league games.
Genoa are on the same points as Fiorentina after winning 3-0 on Saturday against Torino, who slip into the drop zone.
