The game was watched by Manchester United Sir Alex Ferguson, whose side face Milan in the Champions League next month, and he will have taken note of the way Inter almost blew Milan away prior to Sneijder's dismissal.
True, Milan were without central defender Alessandro Nesta, who had failed to recover from a leg muscle injury, and his reassuring presence was sorely missed as Inter poured forward in numbers during an electric opening.
Sneijder's dipping shot gave goalkeeper Dida a fright in the third minute and the Brazilian goalkeeper did well to clear a second shot from the Dutchman with his feet.
Sneijeder should have put the Serie A leaders ahead soon afterwards when the ball deflected into his path but his shot was straight at Dida who cleared with his feet.
But there was nothing he could do to stop Inter's opener when Milito chased down Ignazio Abate's weak header and fired a shot across the Brazilian and into the net.
With the exception of Ronaldinho, Milan were impotent and Beckham's primary contribution in the first half was to pick up the game's first yellow card for a late challenge on Esteban Cambiasso.
The game's second booking - shown to Lucio for a dive - bizarrely led to Sneijder's dismissal.
Beckham and Ronaldinho never managed to inspire Milan
Moments before the Dutchman had been angered when referee Gianluca Rocchi accidentally got in his way ensuring Sneijder lost possession.
He was still fuming when Lucio was booked and picked a straight red card for angrily remonstrating with Rocchi as well as sarcastically clapping the referee.
A disbelieving Sneijder, who had been the focus of Inter's dynamic start, had to be accompanied off the pitch by some of his team-mates, while a grim-faced Inter coach Jose Mourinho prowled the touchline.
Never one to shy away from confrontation with officialdom, the Portuguese was quick to have his say to the referee when Rocchi blew for half-time.
Mourinho's Milan counterpart Milan coach Leonardo introduced Clarence Seedorf at the start of the second half and it was the Dutchman who forced Cesar to make his first save of the game following a corner.
Ronaldinho, who was Milan's most impressive player, then went close with a shot as Inter started to come under sustained pressure.
Beckham also began to come into the game and Marco Borriello should have done better with a header from a cross whipped in by the England international.
Just as it seemed that Milan were about to get back into the game, Pandev provided the cushion of a second goal.
Just beforehand, the Macedonian's clever run had enabled him to beat the offside trap and he was desperately unlucky as his chip came back off the post.
But when he stepped up to take a free-kick Pandev's judgement and delivery was close to perfection as he flighted the ball over the Milan wall and into the net.
There was one final twist to this absorbing encounter when Lucio was red-carded for handball, but the Inter defender was rescued by his Brazilian international team-mate Cesar who superbly turned away Ronaldinho's penalty.
The win ensured that Mourinho's remarkable eight-year unbeaten home run - with Porto, Chelsea and Inter -remains intact.
If Ferguson will have been unduly concerned by the threat Milan will pose United, Inter provided plenty of evidence that they could trouble Chelsea in the Champions League in February.
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