Spurs advanced to the quarter-finals after another night of unrelenting tension at White Hart Lane and the London club's unlikely adventure among Europe's elite continued.
Milan's big-name players like Zlatan Ibrahimovic, Robinho, Alexandre Pato and the evergreen Clarence Seedorf fought non-stop but despite creating the better chances they failed to make the last eight for the fourth successive season.
Spurs, who won 1-0 at the San Siro with a late Peter Crouch goal, could not press home their advantage but the Premier League side gave a resolute defensive performance to reach the quarter-finals of Europe's premier competition for the first time since getting to the European Cup semis in 1962.
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"It's a fantastic achievement for this club, playing in the Champions League for the first time in our history. To have beaten Inter Milan in the group stage and now AC Milan, well anything else is a bonus now, just being in the Champions League is a bonus," Spurs manager Harry Redknapp told reporters.
"Two years ago no-one would have believed we could do this, that's the improvement we have made."
Milan coach Massimiliano Allegri said he was "very very disappointed" his side lost.
"I thought we played very well, we made all the chances, the players worked very hard and the only mistake we made is that we did not score a goal and that's what we have been punished for," he said.
"So from tomorrow morning we will focus on winning the Serie A title. I think we deserved more, because apart from the first half of the first leg we were the better team."
He also defended the performance of Ibrahimovic after being criticised by Italian journalists as being the worst player in the Milan side.
"He is a great player, he played very well tonight, brought his team mates into the play and worked very hard. But if I have any regrets, it's that we deserved more out of the tie. I feel bitter about that."
Redknapp conceded that Spurs were outplayed in midfield but he praised his young Brazilian defensive midfielder Sandro.
Sandro, 21, provided much of the steel Spurs needed to repel Milan's attacks, but when they got past him, central defenders William Gallas and Michael Dawson held firm and goalkeeper Heuerlho Gomes, despite one or two typically eccentric flaps, gave a largely assured performance.
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