The Nigerian international forward scored a goal in each half of the game to help CSKA extend their lead at the top of the Russian Premier League.
Musa latched onto a through ball from Alan Dzagoev to open scoring in the 35th minute. The lead however lasted for only nine as Aras Ozbiliz converted a penalty to level the scores, after CSKA's goalkeeper Igor Akinfeev was adjudged to have brought down Ibrahima Balde.
Musa struck again in the 51st minute to restore CSKA's lead after slamming in a rebound of Dzagoev's shot which was saved by Kuban's goalie, Alexander Belenov.
CSKA sealed the win with another goal six minutes later, as Swedish midfielder Rasmus Elm curled in a screamer from 30 yards out.
CSKA are now four points ahead of Anzhi Makhachkala, who face Lokomotiv Moscow on Sunday.