Atletico had the ball in the net inside six minutes through former Spurs transfer target Ademola Lookman, who tapped in a low cross from Giuliano Simeone, but he was quickly denied by an offside flag.
On the half-hour mark, Spurs broke the deadlock on the night. Mathys Tel's cross following a quick throw-in found Randal Kolo Muani peeling away at the back post, and he rose high to head home.
Tottenham's tails were up and they nearly had a second soon after when Xavi Simons teed up Tel, only for his effort to be pushed aside by a smart save from Juan Musso, who started in place of the injured Jan Oblak. On the stroke of half-time, Guglielmo Vicario was forced into a fantastic save after Simeone's half-volley took a wicked deflection off Cristian Romero, and the Italian had to adjust his body mid-flight to get a strong hand to the ball.
The tie escaped Spurs' grip again on the other side of half-time. The hosts were aggrieved when Simons was bodied to the floor by Julian Alvarez on the edge of the Atletico box, but a foul wasn't called and the visitors broke at pace before Alvarez arrived late to sweep a shot into the top corner, and the goal was allowed to stand after a VAR check.
But Simons had his redemption moments later when he put Tottenham ahead again. Spurs won possession back high up the pitch, and Archie Gray laid the ball off for Simons to curl in from the edge of the penalty area.
Any lingering hope of a late comeback was killed for good 15 minutes from time when Atletico scored from a corner, with David Hancko ghosting in ahead of Pape Matar Sarr at the front post to equalise. In the final minute, however, Spurs were awarded a penalty when Simons was taken out by Jose Maria Gimenez, and Tottenham's No.7 stepped up and converted to ensure the hosts at least won the second leg.
The other silver linings for Tottenham are they extended their unbeaten home run in Europe to 25 games and have shown in their last two matches, against Liverpool and Atletico, that this is not a side that should be battling Premier League relegation, with attention now switching to Sunday's showdown with rivals Nottingham Forest.
GOAL rates Spurs' players from Tottenham Hotspur Stadium...