CSKA striker Alan Dzagoev gave the visitors a surprise early lead but goals from Dele Alli and Harry Kane put Spurs in front at half-time before an Igor Akinfeev own-goal completed a comfortable victory.
“We’ve learned to be better at home. You have to win your home games — you can’t rely on away results,” said Kane.
“We’ve finished the campaign well, there’s a bit of pride to send the fans home happy.”
Tottenham’s hopes of reaching the last 16 had already vanished but this result means they finish third in Group E and drop into the Europa League.
It also ends the club’s miserable six-game losing streak at Wembley, where they will continue to host games in the Europa League and, more importantly, are due to play all home fixtures next season.
Wembley has proven the undoing of Spurs’ Champions League campaign, with consecutive defeats to Monaco and Bayer Leverkusen proving ultimately fatal to their hopes of progress, but at least this dominant display will offer some encouragement they can eventually make the place feel like home.
The attendance of 62,034 was more than 20,000 down on the 85,512 — a record for an English club at home — that turned out to watch Spurs lose to Leverkusen under the iconic arch.
They may struggle to attract similar crowds in the Europa League, which has proven so difficult to balance with the Premier League in recent seasons and where the team have failed to go past the quarter-finals in any of their last eight attempts.
A recurring theme of Tottenham’s Champions League campaign has been paying the price for missed chances and it looked like a repeat was on the cards here when Dzagoev gave CSKA the lead with their first shot on target.
For the previous 32 minutes, Spurs had dominated their opponents in terms of both possession and chances but they just lacked that killer instinct when the goal appeared at their mercy.
Alli and Christian Eriksen were the most influential but also most guilty, the former heading the latter’s cross wide early on and then Eriksen should have scored when played through by Kane, but instead shot straight at Akinfeev.
Tottenham continued to pour forward with purpose but Alli failed to finish another golden opportunity after Eriksen had flicked Danny Rose’s quick throw into his path, Akinfeev this time collecting a scuffed half-volley.
There was some inevitability in CSKA punishing Spurs’ wastefulness although they also enjoyed a stroke of luck as Zoran Tosic looked offside when he headed on a long ball for Dzagoev to drive past Hugo Lloris.
A deflated hush enveloped Wembley but before any frustration could grow, the home side were level.
This time Kyle Walker looked offside as he played in Eriksen, whose lifted cross to the back post was misjudged by Kirill Nababkin, allowing Alli time to touch down and bend the ball into the far corner. It was his first goal in nine appearances.
Tottenham were back in charge and on the stroke of half-time they took the lead, Eriksen again involved as his ball set free Rose, who crossed first time for Kane to tap into an open net.
In the second half, Pochettino introduced first the rarely-used Georges-Kevin Nkoudou and then Toby Alderweireld, who drew the most enthusiastic cheer of the night as he took to the field in the 68th minute for the first time in almost eight weeks following a knee injury.
Alli ballooned a finish over the bar soon after and Eriksen hit the post with a free-kick, before scooping the ball over the top, only for Akinfeev to deny Kane’s volley.
The CSKA goalkeeper, whose Champions League record streak without a clean sheet now stretches to 39 games, looked to have pulled off another strong save when he clawed out Alli’s free header with 13 minutes left. The ball, however, cannoned off his right foot and into his own net. It sealed a miserable night for CSKA, whose manager Leonid Slutsky will now leave the club, while Spurs enjoy some Wembley success.
Lloris, Walker, Dier, Vertonghen, Rose, Son (Nkoudou 61), Wanyama (Alderweireld 68), Winks, Eriksen, Alli, Kane (Onomah 82).
Akinfeev, Nababkin, Vasili Berezutski, Alexsei Berezutski, Schennikov, Tosic (Gordyushenko 70), Dzagoev, Bebras Natcho, Milanov, Golovin (Fedor Chalov 46), Traore (Strandberg 79).
Nicola Rizzoli (Italy).