The win stretched CSKA's lead over champions Zenit St Petersburg to eight points with eight games left. Big spenders Anzhi Makhachkala are third, a further two points adrift.
Vagner, CSKA's leading scorer since the break-up of the Soviet Union in 1991, set up Alan Dzagoyev for the first goal in the 25th minute.
Early in the second half the flashy Brazilian, who sports distinctive braids in the club's red-and-blue colours, scored his first goal since returning to Moscow from his native country in January to start his third spell at the army side.
He made it 3-0 with a 70th-minute penalty before Ivory Coast striker Seydou Doumbia, who has just returned after missing most of the season with a back injury, completed the rout in added time.
Vagner also forced a professional foul from Alania's Brazilian defender Welinton, who was shown a straight red card shortly after the striker had put the visitors ahead 2-0.
Despite the comfortable victory, CSKA coach Leonid Slutsky warned his team against over-confidence.
"I don't want to talk about the championship before the last match is played," he told Russian television NTV Plus.
"Even today, despite the lopsided score, it wasn't an easy game. Alania made us work very hard in the first half."
The defeat extended Alania's winless streak to 17 games as the team, coached by former long-serving CSKA boss Valery Gazzayev, remained rooted to the bottom of the table, five points from the safety zone.
On Sunday, Zenit beat Chechen side Terek Grozny 3-0 to keep alive their slim hopes of retaining the title while Anzhi crashed to a 4-0 defeat at FK Krasnodar.
The Terek match was played at Anzhi's home arena in the neighbouring Northern Caucasus region of Dagestan after they were hit with a ground ban after Chechnya's strongman leader Ramzan Kadyrov insulted a referee over a loudspeaker in their previous home game against Rubin Kazan.
With Kadyrov's blessing, Terek ordered 400 buses to take some 20,000 die-hard supporters on a 165-km trip to Makhachkala but the fans were left hugely disappointed as their team lost for the third time in four matches and had a player sent off for a second successive game.
In Krasnodar, Guus Hiddink's Anzhi, who were missing several leading players through injury including captain Samuel Eto'o, suffered their heaviest defeat of the season with Brazilian striker Vanderson scoring a hat-trick for the home team.