The Belgium international made two world-class saves to keep his side's chances alive before the powerful striker netted a vital away goal.
Atleti was pinned back in its own half for large spells of the game, with Mario Balotelli in particular impressing for the Rossoneri, and the final result was rather flattering for Diego Simeone's men.
It's no coincidence that the Vicente Calderon side finds itself in pole position to make it to the quarterfinals of the competition, though. While Mesut Ozil failed to hand Arsenal the initiative in the club's tie with Bayern Munich as he spurned an early penalty, Atletico's star players did deliver when it mattered most.
"In the first half, Thibaut Courtois' performance was fundamental. In the second, it was Diego Costa who made the difference by taking advantage of the chance that came to him," Simeone said at the post-match press conference.
COURTOIS SAVES THE DAY
FROM OUR LIVE COMMENTARY
Milan fashion the first genuine opening of the match and my goodness did they go close. Taarabt plays in Kaka with a diagonal ball into the area, and the Brazilian smashes the ball towards goal. But Courtois makes a MAGNIFICENT save, brushing the ball with his fingertips onto the crossbar!
COURTOIS IS ABSOLUTELY SPELLBINDING AGAIN! Taarabt again is running things for the Rossoneri, and he whips in a dagger ball to Poli inside the area. The former Inter man impressively flicks a header towards the far side, but an INHUMAN dive from Courtois sees him claw the ball onto the woodwork for the second time!
The real star of the show, however, was Courtois as the Chelsea loanee pulled off two fantastic saves in the first half.
The 21-year-old first showed his class in the 14th minute as he diverted a Kaka shot onto the crossbar, and the former Genk man again confirmed his status as one of the rising stars of football only five minutes later. Andrea Poli must have been convinced that he had given Milan the lead with a well-timed header from Adel Taarabt's cross, but Courtois managed to tip his attempt against the post with unnatural reflexes to keep it all square at San Siro.
Some 960 kilometers away from Milan, Bayern goalkeeper Manuel Neuer – widely regarded as the best in the world - was putting in a breathtaking performance in London as he kept the titleholder in the race against Arsenal, but Courtois was at least as important for Atletico - a feat quickly acknowledged by Costa.
"Courtois is one of the best goalkeepers in the world and he knows it. With a keeper like him, we feel more secure," the match-winner said of the Belgium international after the game.
Courtois might have been deemed not yet ready for Chelsea at the start of the season, but he continues to perform at an admirable level, both in La Liga and in the Champions League, and he could be key to Atletico's chances of European success.
With Costa finding his scoring boots again after slow start to 2014, Simeone will be confident of killing off the tie with Milan at the Calderon in three weeks' time.
From there on, anything seems possible for Atletico as long as the team's stars continue to rise to the occasion at the biggest moments - just like they did on Wednesday.