Only goalkeeper Hugo Lloris was retained in the starting line-up from Spurs' 2-2 draw at Sunderland last weekend for the Group C in clash in Belgrade.
The changes may have played a part in what was a somewhat lacklustre showing from Mauricio Pochettino's men, who saw plenty of the ball but created little in terms of clear-cut chances.
Spurs' best opportunity of the first half came in the second minute when Harry Kane saw an effort cannon off the crossbar.
Partizan, who have scored 18 goals on their way to five straight wins to start their domestic campaign, were effective on the break and the lively Danko Lazovic saw a close-range shot denied by Nabil Bentaleb's timely block midway through the first half.
The second half also failed to produce much in terms of goalmouth action as the match petered out into a draw.
It could have been a different story had Kane not seen his early strike hit the woodwork. The 21-year-old collected the ball at the back post from a corner before shifting onto his left foot and crashing a shot against the frame of the goal from close range.
Spurs showed plenty of patient build-up play but were often frustrated by a solid Partizan defence, while the hosts appeared happy to sit deep and play on the counter-attack.
That tactic almost proved fruitful when Miroslav Vulicevic's cross from the right found Lazovic, but the forward could not sort his feet out and the ball went harmlessly wide.
Partizan then had a great chance in the 25th minute.
Debutant Federico Fazio completely misjudged Vladimir Volkov's long throw into the area and Bentaleb charged across to make a fine block from Lazovic's first-time volley.
From there the chances dried up somewhat, but Partizan had one last opening on the stroke of half-time when Danilo Pantic shot straight at Lloris from the edge of the area following a swift break.
Partizan stepped up a gear at the start of the second half and Petar Grbic should have done better when he shot tamely at Lloris following fine hold-up play from Lazovic.
Lazovic himself had another sight of goal soon after, but this time it was Fazio who came across to make a last-ditch block.
Tottenham introduced Roberto Soldado and Erik Lamela shortly after the hour mark in an attempt to find more creativity in the final third.
Grbic was proving difficult for Spurs to deal with in the second half and, with 15 minutes remaining, his cross from the right picked out Sasa Ilic who stooped low to meet the delivery but headed well over the crossbar.
Neither side could find the breakthrough in the closing stages and Spurs will now look for their first pool win at home to Besiktas on October 2, while Partizan next face Asteras Tripolis.
