Ramos makes winning CSKA start
After a hesitant opening, Czech forward Tomas Necid struck 12 minutes into the second half. Brazilian substitute Guilherme added two more to give Ramos a perfect start.
Former Real Madrid, Sevilla and Tottenham Hotspur coach Ramos replaced Brazilian Zico, who was sacked by the army club on Thursday following a string of poor results.
The win lifted CSKA into third place above city rivals FK Moscow, who slumped to a 2-0 home defeat to struggling Amkar Perm.
CSKA, who face German champions VfL Wolfsburg in a Champions League Group B opener on Tuesday, still trail league leaders Rubin Kazan by 10 points with nine matches left.
Russian champions Rubin warmed up for their debut in Europe's premier club competition by hammering Saturn Ramenskoye 5-1 and stay top of the table with 46 points from 21 matches.
Spartak, in second place on 39 points, meet city rivals Dynamo in a Moscow derby on Sunday.