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.