Making just his seventh appearance since crossing from Montpellier on transfer deadline day, Stambouli fired home from close range after Roberto Soldado's chip had hit the post.
And the French midfielder's 49th-minute strike proved enough for Tottenham to secure their spot in the competition's last 32 on a night where three separate pitch invasions saw the match temporarily suspended in the first half.
Play resumed after a short break but Spurs could yet face sanctions from UEFA following the numerous interruptions.
Tottenham's qualification from Group C means top spot will be up for grabs when they visit Besiktas on matchday six. Spurs are two points ahead of the Turkish side.
Partizan, who were already eliminated prior to this game, round off their campaign with a home clash against Asteras Tripolis - who drew 2-2 with Besiktas on Thursday.
Petar Grbic stormed down the right and saw his cross clip the shoulder of striker Petar Skuletic, while Danko Lazovic chested Sasa Ilic's hooked ball down before shooting narrowly wide under pressure in the 18th minute.
Soldado just missed Erik Lamela's ball across the face of goal but the most animated the White Hart Lane crowd got during a lacklustre beginning was after two pitch invasions in quick succession.
It just was not Soldado's night - he was one-on-one with Partizan goalkeeper Milan Lukac - but could only shoot straight at the onrushing Serbian, while Lamela missed the target on two further occasions.
The competition's joint top-scorer heading into the match - Harry Kane - was introduced as Tottenham head coach Mauricio Pochettino sought to kill the game off with a second goal.
Kane quickly produced a powerful free-kick, only for Lukac to be equal to the task, and the England Under-21 forward also had an effort correctly ruled out for offside with seven minutes left.
Spurs then had Lloris to thank as, with four minutes left, the Frenchman made an outstanding reaction save to keep out a header from the unmarked Vladimir Volkov.
And the stop proved crucial as Stambouli's goal sealed Tottenham's European progression - despite Lamela fluffing his lines and shooting wide after the Frenchman strangely elected to pass rather than shoot in the dying stages.
