The Serbian's fourth minute strike, from an inswinging Ryan Giggs corner, came courtesy of some poor marking from ex-Arsenal midfielder Patrick Vieira, who gave the defender enough space to place a header beyond Julio Cesar's reach.
For a while Inter were stunned, with temperamental but brilliant forward Zlatan Ibrahimovic not looking in the mood for a scrap, but his 29th minute effort begun a thrilling quarter of an hour spell.
Maicon, who was dangerous going forward from right-back, hit a measured set-piece to Ibrahimovic at the back post, but the Swede's downward header bounced onto the bar and out for a goal-kick.
United were unlucky enough to have their best chance fall to John O'Shea, who looked out of place filling in at right back.
More good work from Giggs found Wayne Rooney in space on the edge of the box and the striker's first-time pass into O'Shea sent the full-back through one-on-one with Julio Cesar, but the keeper rushed out to block the low shot.
For Inter, two decent chances fell for Dejan Stankovic before Ibrahimovic again found himself free after 41 minutes.
An inch-perfect, first-time pass from Mario Balotelli behind the United defence played in Ibrahimovic and the Swede took a touch before striking a shot beyond Edwin van der Sar but just past the post.
Inter would rue that miss as United scored another goal quickly after the restart.
Giggs' run and pass to Paul Scholes found Rooney on the left and the striker's dinked cross was met by Cristiano Ronaldo, who nodded in past Julio Cesar.
It was a fatal blow to the Italian club after manager Jose Mourinho had introduced Sulley Muntari at half-time and set his side off at a fearsome pace.
To their credit the Serie A league leaders maintained an attacking threat and were inches away from pulling a goal back in the 59th minute.
Adriano had been on less than a minute when he hit an Esteban Cambiasso cross on the volley, beating van der Sar, but not his right-hand post.
Ronaldo and Rooney had further efforts that tested Julio Cesar, who impressed as Inter's attacking intent left gaps at the back, but both sides began to settle on a 2-0 result and the game petered out.
United will not worry that they couldn't increase their tally, they did more than enough to see off Mourinho's Inter 2-0 on the night and on aggregate.