Russia international Dzagoyev scored for the third consecutive match when he fired in from close range after the Volga goalkeeper blocked a Rasmus Elm free kick in the 30th minute.
Brazilian striker Vagner, CSKA's leading scorer since the break-up of the Soviet Union in 1991, slid in another rebound for his third goal in the last two games five minutes later.
His brace in a 4-0 rout of Alania Vladikavkaz last weekend were his first goals since he returned to Moscow from Brazil in January to start his third spell at the army side.
However, Vagner, who sports distinctive braids in the club's red-and-blue colours, will have to miss CSKA's next match against bitter city rivals Dynamo after being sent off in stoppage time for a second booking.
"Vagner had already apologised to his team mates and the coaching staff for his ejection," CSKA coach Leonid Slutsky told reporters.
"But I wouldn't blame him too much. He was getting kicked for almost the whole game. The fouls kept coming and he just over-reacted in the end. I'm not going to punish him for that."
CSKA have 55 points, champions Zenit St Petersburg are on 44 with Anzhi Makhachkala in third place, a further two points adrift with eight games remaining.
Zenit face lowly Krylya Sovietov Samara while big spenders Anzhi host bottom team Alania on Sunday.
Also on Saturday, Chechen side Terek Grozny held Lokomotiv Moscow to a 1-1 draw while Spartak Moscow slumped to a 1-0 defeat at mid-table Rostov and also lost Spanish playmaker Jose Jurado to injury in the first half.
Serbian striker Danko Lazovic, who joined Rostov on loan from Zenit in January, slotted home a 50th-minute penalty to give his new team their first win in five games.
Spartak, held by Kuban Krasnodar to a 2-2 home draw last weekend, stayed in seventh place, 18 points off the lead.
"For the second game in a row we look terrible. It seems, the team has lost its will to fight. I have to find out why," said Spartak coach and former Russia winger Valery Karpin.