Joining the hopeful debutants and the holders on the night were Juventus, Bayer Leverkusen and Monaco.
They join last year's runners-up Atletico Madrid, Arsenal, Paris Saint-Germain, Bayern Munich and Borussia Dortmund, who had already booked their tickets to the knockout phase with two group games to spare.
Leicester's success saw the Foxes advance as Group G winners in their maiden season in the event, giving a major fillip to Claudio Ranieri's side, who are just two points above the domestic drop zone.
Referring to his side's poor league form the Italian added: "Maybe we have been more concentrated in the Champions League. Now the group is won, (it is) important to come back in the Premier League."
Shinji Okazaki netted after just five minutes and a Riyad Mahrez penalty made it 2-0 before Jose Izquierdo notched a second-half consolation for Brugge.
"We wanted to finish first in the group. It wasn't easy today but we did it," said Foxes' Algerian star Mahrez.
The Colombian's strike was the first goal Leicester have conceded in the tournament to date.
Spurs had a let off when their French keeper Hugo Lloris saved Radamel Falcao's early spotkick. But quickfire goals from Djibril Sidibe and Thomas Lemar just after the break, sandwiching a Harry Kane penalty, did for the Londoners.
In the same group Bayer Leverkusen drew 1-1 at CSKA Moscow to take the Germans into the knockout stages following Spurs' loss.
Kevin Volland put Leverkusen ahead after 16 minutes before Israeli international Bibras Natcho levelled.
Kane said those games sank them.
"I'm gutted. We wanted to go far but it is something we will have to deal with.
"We will look back and say it was the home games were we should've been better," the striker told BT Sport.
Raphael Varane gave the 'meringues' the lead before
Adrien Silva netted a spot-kick for the Portuguese only for substitute Karim Benzema to pop up with the winner for Real.
"We knew it would be complicated, but we got the three points," said Real coach Zinedine Zidane, who won the 2002 title as a player for the Spanish giants and then as coach last May.
"When you concede a goal you can think it will be tough but we continued to play and responded and finally had our reward with Karim's goal," Zidane told beIn Sports.
Dortmund secured the group win with a game to play after swatting Poland's Legia Warsaw 8-4 -- a record goalfest for a Champions League encounter.
Marco Reus scored a hat-trick and Japanese star Shinji Kagawa netted a brace as Dortmund ran riot.
Two-times champions Juventus are through after defeating previous Group H leaders Sevilla, Europa League champions for the past three seasons, 3-1 in Spain.
Claudio Marchisio with a penalty, Leonardo Bonucci and Mario Mandzucic scored for the 'Old Lady' of Turin after Nicolas Pareja had put Sevilla ahead early on.
Perennial challengers Barcelona and Manchester City were hoping to book their tickets Wednesday with wins over Celtic and Borussia Moenchengladbach respectively.
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