Dele Alli was the tormentor in chief with goals in either half, before Christian Eriksen knocked in a third on the break.
Cristiano Ronaldo netted a consolation but it was too little, too late for Real who suffered their first group stage defeat for 30 games; dating back to 2012.
And having held Los Blancos at the Bernabeu two weeks ago, the 3-1 success gives Pochettino reason to speculate that anything is possible going forward.
"Victories are important for us and the players and for the fans because it is Real Madrid and they are the best team in the world," he told BT Sport. "It is fantastic to feel that you can compete but it is a long way to the end of the season. we must achieve our target and challenge. We showed it today and must do it again on Sunday.
"It gives great belief to everyone, great confidence. That is so important now. We are into the next stage of the Champions League. It is important that we are two games ahead. But now it is important to be ready to compete against Crystal Palace. But we must move on."
The win, which sees Tottenham join Manchester City, Paris Saint-Germain and Bayern Munich as the only sides to have qualified for the knock-out phase, came at a cost however with Toby Alderweireld going off with a suspected hamstring injury in the first half.
Goalkeeper Hugo Lloris played the full 90 minutes but will also be assessed having picked up a groin injury during a clash in the Spurs box. But one positive for the north Londoners was the fitness of Harry Kane who returned from missing two games with a hamstring injury to play 80 minutes against the holders.
"It is important that Harry Kane feels good," added Pochettino. "We feel a little bit bad for the injury to Toby Alderweireld. We must assess Lloris too. When it is a period when we must compete it is always tough for the players.
"My final decision is always my final decision but we share with the medical staff. It is always about playing without risk and today was not a risk. It was important to keep him away for two games and for him I am so happy because his performance was good and he finished the game after 80 minutes in good condition."