Croat forward Zvonimir Boban scored the opener in the 41st minute on a fast counterattack. Italian veteran Daniele Massaro made it two with a perfect header in the 65th of the first game played in Italy since the Jan. 29 stabbing death of a fan.
The second leg goals by the Italian champions were decisive following a goalless draw in the first leg at Highbury last week.
It was the third Super Cup victory and the 13th International trophy for the Milan powerhouse which is owned by former Italian premier Silvio Berlusconi.
Milan supporters kept almost silent during the first half, in a sign of respect for the Genoa fan stabbed to death prior to a league game 11 days ago.
The murder prompted suspension of all sports in Italy last Sunday.
In the second half of the game the fans supported the home team with usual chants and applause.
The yearly European Super Cup features the winners of the two most titled European competitions.
Milan is the holder of the 1994 Champions Cup. Arsenal won the Cupwinners' Cup last year.
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American goalkeeper Kasey Keller produced a match-winning penalty shootout save Wednesday, as division one Millwall knocked out Premier League Chelsea to reach the fifth round of the English F.A. Cup.
The game went to penalties with the two teams tied at 1-1 at Stamford Bridge after extra time. With Millwall 5-4 ahead in the shootout, Keller made the only save from Chelsea's John Spencer.
Millwall ousted Premier League Arsenal in the previous round, again in a replay on the road and has now knocked out last season's beaten finalist. It meets another London team, Queens Park Rangers, for a place in the last eight.
After the game, a large number of fans invaded the field and mounted police moved quickly onto the playing area in an attempt to prevent violence breaking out. 38 fans were arrested and 11 police officers were injured in the melee.
"Missiles were being thrown and we believe tear gas was used against officers," said a Scotland Yard spokesman, speaking on condition of anonymity.
Scotland Yard said at least two police officers were taken to the hospital with head injuries. Nine others suffered minor injuries, including cuts and sprains.
In another upset Wednesday, Chris Waddle's 1990 World Cup nightmare returned as he missed a shootout penalty and division one Wolves, now managed by former England coach Graham Taylor, eliminated his Sheffield Wednesday team at Molineux.
With the two teams also tied at 1-1 after extra time of a replay, Wednesday went into a 3-0 lead in the shootout through Mark Bright, Guy Whittingham and even goalkeeper Kevin Pressman. But Wednesday threw it away.
While they missed from the spot, Wolves' veteran midfielder Gordon Cowans, striker David Kelly and Dutch defender John de Wolf tied the penalties at 3-3 before Waddle's kick for Wednesday was saved by Wolves 'keeper Paul Jones. Don Goodman then made no mistake as Wolves advanced 4-3.
Waddle's most famous penalty miss came in the World Cup semifinal against Germany in 1990 in Turin. That miss, also in a shootout, helped put Germany, and not England, into the final.
In other fourth round replays, Southampton overwhelmed another division one team, Luton, 6-0 and Norwich needed two extra time goals to down Coventry 3-1.
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