It was the first time that Milan, the seven-time champions which had reached the quarterfinal stage for the past five seasons, had lost to an English team at San Siro. "It's good for such a young team to beat a team like Milan with so much quality," Arsenal manager Arsene Wenger said. "It will be positive for the future and the rest of this season."I have a big respect for Milan. It can happen that you lose at home. It happens to everyone."Arsenal qualified 2-0 after the two teams drew 0-0 in the first leg in London two weeks ago
"There are no regrets," Milan coach Carlo Ancelotti said. "There are regrets when you could have done more, but they didn't allow us to. Both sides did their best and we have to accept the loss and move on."
Milan president Silvio Berlusconi said Ancelotti would "absolutely" remain the team's coach.
Fabregas scored with a long bouncing shot from outside the area in the 84th minute that beat Milan goalkeeper Zeljko Kalac. The ball may have deflected off the arm of Milan defender Alessandro Nesta.
Adebayor added the second goal from close range in injury time after the ball was crossed into the box from the right flank.
In its 11 previous home games against English teams, Milan had won seven and drawn four, including a 2-0 win over Arsenal in the 1994 UEFA Super Cup.
"For us, it's just the beginning," Fabregas said. "Now we are in the quarterfinals. We haven't done anything. It's just one more step for the season. We will try to go on until the end but now focus again on the league which is very important."
Wenger said his plan to use Fabregas and Mathieu Flamini to contain Kaka worked to perfection.
"We decided not to give him time on the ball and it turned out that we decided well," Wenger said.
Milan started the game at a high tempo, pressing in defense and creating several good chances inside the first 25 minutes.
Alexandre Pato dribbled around three players in the eighth minute, but then shot over the crossbar. In the 19th, Kaka went on a long dribbling run before passing to Pato, who hit a soft shot straight to goalkeeper Manuel Alumnia.
But Arsenal soon got back into the game. Adebayor's powerful shot in the 28th was tipped over the bar by Kalac, and Fabregas hit the bar from just outside the area six minutes later.
Arsenal midfielder Aleksandr Hleb was cautioned in the 33rd for simulation just outside the area, although it appeared that he had been fouled from behind.
Milan fielded an attack of Filippo Inzaghi and the 18-year-old Pato, with Kaka just behind the strikers after missing the last few league games with a knee injury. Alberto Gilardino came on in the 69th for Inzaghi, but was unable to spark the Milan attack.
Midfielder Andrea Pirlo and defender Alessandro Nesta had strong games after also coming back from injuries. The Rossoneri were without Clarence Seedorf, who had played in all of the previous Champions League games this year.
Arsenal was without striker Eduardo de Silva, who broke his leg last month, while Robin van Persie was on the bench after a long-term thigh injury.
In the 75th, Kalac made a sliding save with his legs on a close-range shot by Theo Walcott, who received the ball alone at the edge of the box after coming on as a substitute four minutes earlier .
Arsenal leads the Premier League by one point ahead of Manchester United. The Gunners had not won in four matches, including the first-leg draw with Milan and a 4-0 FA Cup loss to Man United.