A Diego Costa header seven minutes from time at San Siro ensured the Spanish side will defend a 1-0 lead in the second leg of their last 16 tie at the Vicente Calderon on Tuesday.
Clarence Seedorf's side have endured a tough campaign, with the Dutchman making a mixed start to his coaching career since the departure of Massimiliano Allegri in January.
Seedorf was at the helm when Milan crashed out of the Coppa Italia to Udinese, while a total of 13 points from a possible 24 under his stewardship has not been enough to lift Milan out of a mid-table position in Serie A.
Therefore, Seedorf must oversee success against the team of old playing foe Diego Simeone to keep alive his chances of tasting success in his first season at the helm.
Milan come into the clash off the back of a disappointing 1-0 defeat to Udinese on Saturday.
However, the likes of Kaka and Adel Taarabt were left out of the starting line-up for that encounter, with the latter - together with Michael Essien and Mario Balotelli - playing a cameo role ahead of Tuesday's trip to Madrid.
"We need to continue working hard, believing that we're on the right track ahead of Tuesday. We'll give our responses out on the pitch," Seedorf is quoted as saying by Milan's official website.
"I'm not worried. We need to think positive and be optimistic.
"We need to be convinced about our abilities to give a good performance and turn the situation around."
While Milan are not challenging for their domestic title, Atletico remain firmly in contention for La Liga glory after David Villa's quickfire brace earned a 2-0 win over Celta Vigo on Saturday.
That success was Atletico's first since beating Milan and Simeone's men were able to pick up three points without the suspended Costa - who will return to action in midweek.
Costa has five goals in four European outings this season and his presence will bolster an Atletico side looking to secure a first Champions League quarter-final appearance since 1997.
Atletico conceded just one goal at home in the group stages, scoring nine, and former Argentina international Simeone feels Saturday's win has provided the club with a welcome lift.
"This feeds the group's confidence and we're looking good for the end of the season," he said.
"We were thinking about winning (Saturday's) match because it was very important (but) there will be time to prepare for the match on Tuesday."
While Milan's leading goalscorer Balotelli and defender Cristian Zapata made their return in Saturday's defeat, Seedorf will be without captain Riccardo Montolivo due to suspension.
Tiago and Javier Manquillo are Simeone's main absentees, the former suffering knee and wrist injuries in the La Liga defeat to Almeria last month and the latter fracturing a vertebrae in the Madrid derby.
