England striker Harry Kane headed the only goal of the game, his ninth strike in six matches, with just 12 minutes remaining, while Son Heung-min and Dele Alli both hit the woodwork.
Leaders Spurs lie three points ahead of second-placed Anderlecht and need a solitary point from their final Group J fixture against Monaco on 10 December to seal top spot.
“We are very happy because with patience and maturity we got the win and qualified,” said Pochettino, whose charges face Chelsea in a Premier League tussle at White Hart Lane on Sunday.
“We have to say thank you to our fans as well. To travel here and support us is fantastic and so valuable to us. We have a strong mentality and our fans do too. We will have a great atmosphere on Sunday for Chelsea.”
Kane, who has started Tottenham’s last 41 Premier League matches, scored to continue his blistering goalscoring form, a far cry from early in the campaign when he appeared to be flailing, having notched just three in seventeen.