Midfielder Taulant Xhaka sped past CSKA's sluggish backline and unleashed a powerful low drive that beat veteran goalkeeper Igor Akinfeev in the right corner to put Basel up in the 29th minute.
Basel thought they had scored another early in the second half when Albian Ajeti's drive beat Akinfeev, but referee Bjorn Kuipers ruled offside. After a string of missed chances, Dimitri Oberlin added another for Basel in the 90th minute.
The disallowed goal re-energised CSKA but they were unable to use the momentum to get on the scoresheet.
CSKA's best chance came in the 76th minute when a powerful header by Mario Fernandes floated just over the bar.
Both sides were cautious early in the match, failing to set the pace and create space to generate scoring opportunities.
Basel set-pieces that could have unsettled CSKA were off target or floated into the hands of Akinfeev. But the Swiss side succeeded in shutting down CSKA's offence and conceding no shots on target.
Basel climbed to second place in the group on six points, three behind leaders Manchester United. CSKA are third on three.
(Reporting by Gabrielle Tétrault-Farber; Editing by Ed Osmond)
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