Pato scored an early second half brace following Vucinic's first half opener for the hosts but the Montenegran had the last word with a timely equaliser to deny Beckham a winning start to life in Italy. Milan stay third, nine points off top, while Roma remain in the bottom half of the table.
Milan coach Carlo Ancelotti sprung a surprise by selecting Beckham in his starting line-up. The former England captain took a little time to settle before gradually coming into the game and becoming increasingly involved.
His first opportunity to shine could have come on five minutes after Milan won a free-kick in a dangerous position but Ronaldinho pulled rank and crashed his effort into the wall. Thereafter Beckham showed his full range of abilities, playing one raking ball down the line to Kaka while showing his defensive skills in making a brilliant sprawling block on a John Arne Riise shot.
He also sent many dangerous crosses in from the right. "I decided to start with Beckham because he had demonstrated over the last few days that he was intelligent, serious and committed. This was his reward for settling in so quickly," said Ancelotti. "I will never tire of pointing out that he is an exemplary professional who works hard."
Roma were battling to get back into Champions League contention after a torrid start to their season and on 22 minutes Vucinic broke the deadlock, latching onto a cross from Riise, turning Marek Jankulovski far too easily on the edge of the six-yard box and slotting home past Christian Abbiati.
In the first minute of the second half Roma captain Daniele De Rossi made space just outside the box but shot well over. And just two minutes later the hosts were made to pay as Philippe Mexes was pulled out of position and Kaka crossed for Pato to tap home from two yards out.
And Pato scored an equisite second on 53 minutes as Ronaldinho released him down the left before the teenager outstripped Mexes and then chipped Doni. However, Roma hit back 19 minutes from time as Vucinic bagged his second with a diving header after Matteo Brighi's shot was deflected into his path. Beckham, obviously tiring, was substituted two minutes from time.