The European Cup holders scored two goals within the first four minutes of each half as Sir Alex Ferguson recorded only his second win over Jose Mourinho.
Nemanja Vidic headed past Julio Cesar from a Ryan Giggs corner after just fout minutes, before Cristiano Ronaldo sealed the win just after the interval when he too nodded home after good work by Wayne Rooney.
United did not have it all their own way, however, as Inter, much improved from the first leg, hit the woodwork twice through Zlatan Ibrahimovic and Adriano.
United began the game confidently and looked to get Ronaldo on the ball as much as possible in a bid to take advantage of the inexperienced Davide Santon at left-back.
It was an early foray down the right hand side form the Portuguese winger, which earned his side a corner, which brought about the opening goal.
Giggs trotted across to whip the ball in and he found Vidic, who took advantage of some slack marking by Patrick Vieira, to power a header past Cesar.
United could have doubled their lead on 18 minutes when Giggs got in behind Maicon but, with only Dimitar Berbatov to aim for, his cross was cut out by Walter Samuel as the referee waved away protests of hand ball.
Berbatov had been a doubt immediately before kick-off after going over on his ankle in the warm-up, but the Bulgarian appeared to have shaken off the problem as he looked lively early on.
Over confidentThe hosts began to look over confident as both Giggs and Paul Scholes were guilty of giving the ball away in dangerous areas.
The Welshman's misplaced flick halfway inside the Inter half nearly led to the visitors equalising just before the half-hour mark.
In United's desperation to win the ball back they gave away a free-kick just inside their own half. Maicon crossed and Ibrahimovic headed downwards at the far post only to see his header come back off the bar with Edwin Van der Sar beaten.
Mourinho's men had settled well since their early set-back as the home side went through a sloppy spell ten minutes before the break.
Inter midfielder Dejan Stankovic nearly made them pay when he hit a shot from all of 30 yards that swerved just wide of Van der Sar's left-hand post, with the Dutchman scrambling across his goal.
But United came back and should have made it two on 37 minutes when Giggs drifted in from the right and found Rooney, whose first-time pass cut open the Inter defence and found John O'Shea bearing down on goal, but his effort was saved by Cesar.
Inter immediately went up the other end, with Mario Balotelli mirroring what Rooney had done moments earlier when he duly sliced open the home defence with a first-time pass which sent Ibrahimovic through, but his fierce drive across goal went just wide.
Inter began the second half as brightly as they ended the first as Sulley Muntari came on for Vieira but it was United who got the game's next goal four minutes into the second period.
InfluentialGiggs was again influential as he left a number of Inter players in his wake as he dribbled infield from the right before finding Scholes, who in turn fed Rooney on the left corner of the area.
The 23-year-old teased Maicon before floating a dangerous in-swinging ball with his right foot which was met by Ronaldo, who got their before Cesar, to head into the unguarded net.
Inter were momentarily shaken but began to find their rhythm again just before the hour as Mourinho went for broke by sacrificing Stankovic for Adriano.
The Brazilian produced a moment of magic seconds later when he linked up with Esteban Cambiasso and volleyed left footed, on the stretch, against the post.
Sir Alex Ferguson's men responded and should have put the game out of sight on 59 minutes when Cesar parried a long range Rooney drive straight to Giggs, who laid the ball off to Berbatov but his shot from five yards was smothered by the keeper.
Mourinho made his final substitution of the night with Luis Figo replacing Balotelli, while Ferguson brought Anderson on for Scholes as he looked to close the game out.
But it was the visitors who continued to press as United struggled to keep possession of the ball, however, wayward long-distance attempts from Ibrahimovic and Adriano undermined their impressive approach play.
The Swede may have pulled a goal back had he committed himself to Muntari's deep left-wing cross on 75 minutes. Instead he did not react quickly enough after the ball went over Patrice Evra's head and rebounded off his chest for a goal kick.
1st Half Goals
Shots on Target
Shots off Target