Pontus Wernbloom headed in a corner from Alan Dzagoev to put CSKA ahead in the 38th minute of the game, before Musa added his name to the scoresheet in the 72nd minute.
Returnee Brazilian striker Vangner Love flicked the ball to Musa to set up the goal, and the Nigerian made no mistake in sending a low drive into the far corner of the post to seal the win for the visitors.
"We confidently controlled the course of the match and turned our advantage into goals scored," CSKA coach Leonid Slutsky said after the game.
CSKA Moscow have now extended their lead at the top of the table with 46 points from 20 games.
Second-placed Anzhi Makhachkala have 41 points albeit with a game in hand.