Milito goal sinks CSKA Moscow
Milito rifled in a right-footed shot into the bottom corner from the edge of the box in the 65th minute at the San Siro after a strong run by Wesley Sneijder.
CSKA closed down Inter well in the first half, but showed little ambition as the Italian champions increased the tempo after the break.
The hosts failed to put away a series of chances either side of Milito's goal, with CSKA keeper Igor Akinfeyev making some fine saves. Inter striker Goran Pandev also had an effort cleared off the line.
"Unfortunately, I can't start thinking about the semi-final yet," Inter coach Jose Mourinho told a news conference. "Unfortunately I still have to think about another hard match in Moscow.
"We had chances for a better result - 1-0 leaves the tie open, but we are in front," he said, adding that Inter had "overcome their mental block with the Champions League" after recent disappointments in the competition.
CSKA, who upset Sevilla in the previous round, gave away no signs of stage fright in the early exchanges, with Milos Krasic making a good break down the right straight after kick-off.
Inter, without suspended centre-back Lucio and midfielder Thiago Motta, looked to be struggling to find a way through the Russians' defensive maze.
But they woke up after seeing their keeper Julio Cesar push away a powerful Yevgeny Aldonin effort on one of CSKA's rare foray forward 10 minutes into the second half.
Mourinho's side, who ousted Chelsea in the last 16 but have been in poor form in Serie A recently, had the Russians under unrelenting pressure and Milito gave them their reward.
Akinfeyev did well to deny Samuel Eto'o, Dejan Stankovic and Esteban Cambiasso and Pandev afterwards and Sneijder hit a great chance wide in the closing stages.
Krasic and Aldonin will miss next week's return leg after being booked.
"Today's result could not have been better, but it could have been worse," said CSKA coach Leonid Slutsky, adding that he does not think his club's artificial pitch will give them a big advantage in the second leg.
"The synthetic pitch will not be fundamental for the teams. It has never been unfavourable to our rivals."