After a goaless first half, the game came to life just after the restart as Djibril Sidibe opened the scoring for the hosts before Harry Kane equalised from the penalty spot.
Lemar, though, just as he had done at Wembley, scored the winning goal for the hosts 38 seconds after Spurs had equalised to send the hosts through to the knockout stages. Spurs will have to play for third spot in the group in their final game at home to CSKA Moscow.
Both sides missed early chances
The first half may not have seen a goal but it saw plenty of chances for both teams to take the lead.
Spurs should have gone in front very early on when a lovely through ball from Dele Alli played Son Heung-Min through on goal but the striker took a heavy touch and wasted a brilliant chance to give the visitors a vital lead.
The hosts then came into the game more and they were awarded a penalty a few minutes later when Eric Dier fouled Fabinho in the box. Radamel Falcao stepped up to take it and as he so often does for Spurs, Hugo Lloris made a brilliant save to deny the striker.
Chances kept coming as Valere Germain missed saw a close-range shot saved by Lloris before seeing a goalbound header blocked on it's way to goal a few minutes later.
At times at the back, Spurs were non existent during the half as they badly missed Toby Alderwerield and Jan Vertonghen in the centre of defence to sort everything out.
Spurs kept attacking themselves though as Kane had a big chance at the other end at the back post but he couldn't get the contact on the ball that he was hoping as he miskicked the ball.
Throughout the half, both teams weren't afraid to get their tackles in and if it continued like that throughout the game then someone could have been in bother of getting sent off.
Goals flow at the start of the second half
The second half did see goals though as the home side went in front within three minutes of the restart.
A brilliant run and cross from Benjamin Mendy found Sidibé unmarked in the box and the right back powered his header past the impressive Lloris.
Spurs though responded well to going behind and they were awarded a penalty when Kamil Glik fouled Alli in the box. Kane stepped up to take it and even though Danijel Subašić got his hand to the ball, it went into the net.
Spurs weren't level for long though as straight from the kick-off and 38 seconds later Lemar smashed a lovely left-footed shot into the back of the net after a good cross from Sidibe found the winger in the box.
Lloris saved Spurs blushes on the night as they crashed out the Champions League
Lloris was called into action once again not long after to stop Monaco from scoring a third goal as a free-kick found Glik unmarked in the box but the defender saw his shot somehow saved by the brilliant Frenchman.
Falcao was next to go close to getting a third goal for Monaco but Lloris made yet another fantastic save to keep his side in the game.
Unfortunately though despite trying to go forward and get an equaliser, the hosts stood strong and kept hold of their win to send the visitors out of the Champions League.