The visitors took the lead in the 33rd minute through Alan Dzagoev, who scored from a headed flick-on from Zoran Tošić.
Spurs restored parity shortly afterwards through Dele Alli, and Harry Kane finished a stylish move to put the home side in front before half-time.
An error from CSKA keeper, Igor Akinfeev, gave Spurs a two-goal lead when he guided Alli’s header into his own net.
The victory puts Spurs into the Europa League for the sixth consecutive season.
Champions League Results: Match Day 6
They finished as one of the four best third-placed teams in the Champions League groups, and cannot be matched with a team from England.
Leicester City suffered the worst defeat by an English team in the Champions League after the Foxes lost 5-0 to Porto.
Champions League Table
Claudio Ranieri made 10 changes to his starting XI with Leicester already assured of progressing as Group G winners.
Elsewhere, Marco Reus scored in the 88th minute to earn Borussia Dortmund a 2-2 draw against Real Madrid.
Karim Benzema scored twice for Los Blancos on either side of half-time, but goals from Pierre-Emerick Aubameyang and Reus mean the German giants snatch first position in the group.
Juventus also progressed to the next round as group leaders, after they beat Dinamo Zagreb 2-0 at Juventus Stadium.
Bayer Leverkusen beat Monaco 3-0, but they still finished second behind the French club in Group E.
Who can Manchester City, Arsenal and Leicester face
First let us take a look at the teams who have progressed.
Champions League: Key Dates
Round of 16 Draw: 12 December 2016
Round of 16 first leg: 14-15 and 21-22 December 2016
Round of 16 2nd leg: 7-8 and 14-15 March 2017
Quarter Final first leg: 11-12 April 2017
Quarter Final 2nd leg: 18-19 April 2017
Semi Final First leg: 2-3 May 2017
Semi Final 2nd leg: 9-10 May 2017
Final (Cardiff): 3 June 2017
Arsenal could face: Bayer Leverkusen, Bayern Munich, Benfica, Real Madrid, Porto, Sevilla.
Manchester City could be paired with: Atletico Madrid, Borussia Dortmund, Juventus, Monaco, Napoli.
Leicester City‘s opponents could be: Bayer Leverkusen, Bayern Munich, Benfica, Paris St-Germain, Real Madrid, Sevilla.