Milito struck in the 65th after linking up with midfielder Wesley Sneijder, but Inter missed a number of chances to score either side of the goal despite dominating the game.
Moscow goalkeeper Igor Akinfeev kept his side in the match with crucial saves and while his opposite number Julio Cesar had little to do he had to react quickly to deny Moscow striker Tomas Necid late on.
The second leg will be on 6 April in Moscow.
Inter Milan: Julio Cesar, Maicon, Materazzi, Samuel, Zanetti, Stankovic, Cambiasso, Eto'o, Sneijder, Pandev (Mariga 90), Milito. Subs not used: Toldo, Cordoba, Quaresma, Muntari, Chivu, Arnautovic. Booked: Materazzi.
CSKA Moscow: Akinfeev, Vasili Berezutsky, Alexei Berezutsky, Ignashevich, Shchennikov, Krasic, Aldonin (Rahimic 75), Semberas, Mamaev (Gonzalez 73), Honda (Dzagoev 69), Necid. Subs not used: Chepchugov, Nababkin, Odiah, Guilherme. Booked: Krasic, Aldonin.
Att: 64,500 Ref: H Webb (Eng).