The Gunners led 4-1 from the first leg but were made to work hard for their passage through in the end, as the Red-Blues moved to within one goal early in the second half.
Danny Welbeck struck to continue his good form, however, finding a way through from his side's first attempt on target for a crucial goal, and Aaron Ramsey added a late second to earn a 2-2 draw on the night.
Arsenal failed to get out of first gear in a sloppy first half in which they were unable to come close to testing Igor Akinfeev in the opposition goal.
For the opening 25 minutes it mattered little, as CSKA were also struggling to create any openings as they went in search of a first win in seven attempts against an English opponent on home soil.
A dragged Kristijan Bistrovic shot aside, it took until half an hour in for the first real attempt, with Alexandre Lacazette being picked out in a good position but seeing his shot blocked by Aleksei Berezutski in front of goal.
The visitors were looking a lot less comfortable when Fedor Chalov netted his first Europa League goal of the season, though, giving the Red-Blues something to build on.
A good chance for Bistrovic to add a second before the break came and went, curling the ball wide from the edge of the box, but it was CSKA who had momentum on their side heading into the second half.
The hosts, denied a penalty late in the opening 45 minutes when the ball struck Ramsey's hand, had their third goal of the tie five minutes after the restart through Kirill Nababkin.
Banned for the first leg, the full-back marked his return to the side by blasting home a rebound following some questionable goalkeeping from Cech, who this time parried Golovin's long-range shot into Nababkin's path.
Cech did better from the next attempt, pushing Golovin's free kick wide of the target, with the visitors - now winless in Russia in five attempts - having to hold on.
That switch in formation appeared to work, as Welbeck tucked the ball past Akinfeev after exchanging passes with Elneny - one of two enforced Arsenal changes tonight - with 15 minutes left to play.
Alex Iwobi missed a good chance late on to make certain of things, but Ramsey fared better when racing clean through on goal by lofting the ball over Akinfeev to keep the Londoners on course for silverware.
CSKA MOSCOW (5-3-2): Akinfee; Kuchaev, A.Berezutski, Ignashevich, V.Berezutski, Nababkin; Bistrovich (Natcho 72'), Dzagoev (Vitinho 78'), Golovin; Musa, Chalov (Milanov 79')
ARSENAL (4-2-3-1): Cech; Bellerin, Mustafi, Koscielny, Monreal; Elneny, Wilshere (Chambers 69'); Ramsey, Ozil, Welbeck; Lacazette (Iwobi 77')