Vitinho and Timur Zhamaletdinov scored in the space of eight second-half minutes to snatch a drought-breaking three points for the Russian outfit.
Portuguese champions Benfica had entered the match as heavy favourites against a team which had lost 11 of their past 13 away fixtures in Europe's premier club competition.
New signing Haris Seferovic put the hosts into an expected lead shortly after half-time, but Viktor Goncharenko's side launched an unlikely comeback in the final third of the contest.
Vitinho levelled from the spot before Goncharenko tucked away a rebound to seal the stunning upset with 19 minutes remaining.
Benfica lost a host of stars over the off-season, including Ederson, Victor Lindelof, Nelson Semedo and Kostas Mitroglou and appear to have plenty of work to do if they are to repeat last season's quarter-final effort.
Both sides failed to make the most of their early sights at goal as Alan Dzagoev poked wide from the edge of the area before Eduardo Salvio miskicked an attempted volley from Pizzi's cross.
Russia international Dzagoev went closer in the 18th minute, testing Bruno Varela low to his left, while Igor Akinfeev comfortably dealt with a rising Andrija Zivkovic shot from range.
The visitors defied the weight of possession to again go close through Aleksandr Golovin on the half-hour mark, the 21-year-old fizzing a low effort just past the near post.
Benfica quickly set about responding and almost did so in perfect fashion as left-back Alejandro Grimaldo unleashed a thumping long-range bullet which shaved the outside of Akinfeev's left-hand upright.
CSKA survived another heart-in-mouth moment late in the half, with defender Viktor Vasin fortunate to escape punishment for appearing to drag Seferovic to the ground inside the penalty area.
Seferovic immediately took matters upon himself after the restart by first heading Pizzi's corner around the near post, before classily netting the opener just moments later.
The Swiss striker darted to the near post to meet Zivkovic's low cross and cleverly flicked a first-time finish past Akinfeev.
CSKA refused to be disheartened by the setback and received a lifeline from the penalty spot just after the hour. Benfica full-back Andre Almeida was penalised for blocking Vasili Berezutski's attempt with his hand and Vitinho duly dispatched the spot-kick high to Varela's right.
And the away side forged ahead in the 71st minute as Vasin again caused a nuisance in the area, the centre-back's impressive shot on the turn drawing a low Varela save from which Zhamaletdinov tucked away the rebound.
The home side piled on the pressure over the closing stages, but CSKA held firm to end their long wait for a victory in the competition.
Benfica's next assignment is a trip to face Basel in a fortnight's time, while CSKA host the group's other victorious side in Manchester United.