Mauricio Pochettino's side were already eliminated from the Champions League before Wednesday's final Group E fixture, but they finished on a high note with their first victory at Wembley at the third attempt.
After falling behind to Alan Dzagoev's strike, Tottenham equalised through Dele Alli and Harry Kane netted in first half stoppage-time before goalkeeper Igor Akinfeev's own goal sealed the points.
Tottenham ended third in the group and the north Londoners will enter the Europa League when the knockout stages begin in February.
Playing in the less glamourous of Europe's club competitions, with its gruelling itinerary and far-flung destinations, might be something of an unwanted burden for Tottenham given the potential to damage their Premier League ambitions.
But the Europa League winners qualify for the Champions League so Pochettino's men may yet end up taking it seriously.
"I'm happy. The performance was good because it showed we can win here. That was important for us. It can change the bad feeling at Wembley," Pochettino said.
"Against Chelsea, Swansea and tonight we have played better. We're starting to show our real quality again."
Defeats against Monaco and Bayer Leverkusen in their other group matches at Wembley had played a major role in Tottenham's exit and contributed to a negative feeling about the stadium among players and fans.
But with Tottenham likely to spend the whole of next season as tenants at Wembley while White Hart Lane is redeveloped, Pochettino was keen for his team to make themselves more at home by beating CSKA.
The swathes of empty seats at kick-off suggested many Tottenham supporters had already made up their minds about the Wembley experience.
But the stay-aways missed Tottenham's only emphatic performance of the tournament.
Early on, Alli headed wide from Christian Eriksen's cross before Son Heung-Min's low strike was pushed out by CSKA goalkeeper Akinfeev.
Another flowing Spurs attack saw Kyle Walker feed Kane, whose instinctive first-time pass released Eriksen, only for the Danish winger to shoot straight at Akinfeev.
Alli wasted a good chance to open the scoring when his tame shot from eight yards barely forced Akinfeev to move.
Not for the first time in their strangely lethargic European campaign, Tottenham were punished for a lackadaisical mistake in the 33rd minute.
A high punt towards CSKA's Zoran Tosic should have been easy for Jan Vertonghen, but the Spurs defender allowed his opponent to win the header and Dzagoev, unchecked by Eric Dier, raced onto the loose ball before firing past Hugo Lloris.
Faced with elimination from Europe, Tottenham found an extra gear and Alli equalised five minutes later when he controlled Eriksen's cross on the left side of the penalty area and whipped a fine finish into the far corner.
Tottenham had failed to score more than once in each of their past nine Champions League games, but 30 seconds into first half stoppage-time, they ended that dismal sequence.
Eriksen chipped a pass towards Danny Rose and the left-back's low cross found Kane, who wasted no time dispatching a cool shot past Akinfeev for his seventh goal in his last six appearances.
Having established the lead, Tottenham looked far more composed after the interval and Kane came close to his second goal when he tested Akinfeev with a lunging volley.
Spurs defender Toby Alderweireld, back from a knee injury, came off the bench for his first appearance since October.
And Tottenham wrapped up only their second Champions League win this season in the 77th minute when Alli headed goalwards and Akinfeev saved before accidently nudging the ball into his own net.