Hamza Igamane gave Clement’s men a deserved lead early in the second-half, before the English Premier League side responded through Dejan Kulusevski.
It was a big point, which sees Rangers move onto 11 points in the league phase table, in eighth place, with two games remaining.
Rangers came into the match on the back of four successive victories, which included last month's 4-1 win in Nice in the last Europa League outing.
The manager named four changes from Sunday’s Scottish Premiership match against Ross County with Robin Propper, Ridvan, Nedim Bajrami and Mohamed Diomande coming into the starting XI. Leon Balogun and Connor Barron were named on the bench, with Danilo and Ianis Hagi not in the European squad.
That meant Jack Butland retained his place between the sticks for this one, behind a back four of captain James Tavernier, John Souttar, Robin Propper and Jefte. In midfield, Nico Raskin was joined by Mohamed Diomande, with Nedim Bajrami operating in an advanced position. Hamza Igamane led the line and was supported by Vaclav Cerny and Ridvan Yilmaz.
It was the English Premier League side who got the action underway at Ibrox with Rangers looking for another big performance in the competition.
The Gers started well in the opening period and had their first chance at goal inside the first 10 minutes. James Tavernier did well to block Timo Werner’s advances down the wing to launch the attack before he found Bajrami in the middle of the pitch. He picked out Vaclav Cerny, but his shot was just over the bar.
At the other end, Spurs showed their threat in attack too, as James Maddison cut the ball back to Heung-Min Son who was able to get a low shot away, but Butland gathered comfortably.
Cerny had another opportunity as Ridvan flicked the ball into the path of Hamza Igamane and he found the winger with a lovely ball across the pitch, but it was held by Forster.
It had been a positive first 25 minutes for Clement’s men, and they came close again as Jefte whipped an inviting ball into the box from the left, but Nedim Bajrami, who had made a run into the area, was unable to get a crucial touch to send it goalwards.
With just over half an hour played, there was a pause in play as John Souttar went down with an injury at the half-way line. The Rangers defender was unable to continue and was replaced by Leon Balogun.
Butland pulled off a superb stop in the latter stages of the first half as he blocked Brennan Johnson’s close-range effort, with the flag going up for offside after the chance. In first-half injury time, Rangers were denied an opening goal by Fraser Forster as he matched a strike from Vaclav Cerny after another good bit of build-up play from the Light Blues in what was an encouraging first-half.
Although maybe not getting their rewards in the 45, Rangers wasted no time after to break in getting that crucial breakthrough. With just over a minute played, James Tavernier made strides down the right-flank before delivering a perfect cross into the box which Hamza Igamane hit first time on his left-foot to beat Forster for his fourth Europa League goal.
The noise levels were raised at Ibrox, and Rangers looked to capitalise with Vaclav Cerny coming close to adding a second goal.
Brennan Johnson had a chance for Spurs as they looked to respond on the counter-attack but he could only curl his shot high of Butland’s goal.
Rangers were really piling the pressure on the visitors in the opening period of the second-half as a short corner nearly came off with James Tavernier and Vaclav Cerny combining before sending it towards Hamza Igamane in the box but it was cleared.
Diomande was next to try a strike from distance, finding himself in space on the edge of the box but it was deflected out for a corner.
With an hour played, Spurs manager Ange Postecoglu turned to his bench as the English side looked for a way back into the game. The changes did give the visitors a bit of a lift, and Butland pulled off another big stop as he got a foot on a strike from Pedro Porro to deny an equaliser.
Clement was next to make a couple of changes with just over 20 minutes remaining in the match as he introduced Connor Barron and Dujon Sterling in place of Nedim Bajrami and Vaclav Cerny.
With 75 minutes on the clock, Spurs had a goal back and it was one of their substitutes who got the goal. The ball came across from the right and it was Dejan Kulusevski who sent a powerful hit low into Butland’s left-hand corner.
Another two changes followed for Rangers with Cyriel Dessers and Robbie Fraser coming on for goalscorer Hamza Igamane and Ridvan. It was a huge moment for 21-year-old Fraser, a product of Rangers Youth Academy, as he made his European debut for the club.
There was a big chance for Rangers in the 80th minute as Dujon Sterling flicked Butland’s goal kick into the path of Cyriel Dessers. The striker took a touch beyond a defender to open up space, but it was deflected wide.
Seconds later, Rangers had the ball in the back of the net with Robbie Fraser whipping a cross into the box and Dessers sending it beyond Forster, but the flag was up for offside and the goal was disallowed.
With a share of the points, it was a positive performance from Rangers as attentions now turn to Sunday’s Premier Sports Cup final.
RANGERS: Butland, Tavernier, Souttar (Balogun, 35), Propper, Jefte, Raskin, Bajrami (Barron, 68), Diomande, Ridvan (Fraser, 79), Cerny (Sterling, 68), Igamane (Dessers, 79).
Subs: Kelly, Cortes, Dowell, King, McCausland, Rice, Curtis.
Tottenham Hotspur: Forster, Dragusin, Son, Bissouma (Bergvall, 60), Maddison, Udogie, Gray, Werner (Kulusevski, 46), Johnson (Solanke, 60), Porro, Bentancur (Sarr, 60).
Subs: Austin, Whiteman, Lankshear, Dorrington, Olusesi, Williams-Barnett, Hardy.