Antonio Conte was sent off after Spurs had a last-gasp Harry Kane winner ruled out for offside after a lengthy VAR check.
The hosts were 1-0 down in the first half when former academy player Marcus Edwards slotted past Hugo Lloris from distance after a lovely run from deep.
Rodrigo Bentancur levelled matters in the 80th minute and Spurs looked like they had bagged a dramatic winner at the death.
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Deep into stoppage time, Emerson Royal's header across goal deflected into the path of Kane, who fired in to send Spurs fans into raptures.
It looked like it was going to be the goal that secured qualification to the round of 16 with a game to spare.
However, there was a good four minute VAR review as a check determined whether Kane was offside.
Eventually, the new semi-automated offside technology ruled that Kane was fractionally off and so the goal was chalked off.
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That prompted protests from Conte and his coaching staff, with the Italian shown a red card and sent down the tunnel.
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It finished 1-1 and Spurs' bid to reach the knockout stages will go down to the final game next week after Europa League holders Eintracht Frankfurt beat Marseille 2-1.
Spurs are still top of the group going into what promises to be an incredible matchday six in Group D, where there are just two points between first and fourth.
Tottenham travel to Marseille, while Sporting host Frankfurt as second meets third in Lisbon.
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It's still in Spurs' hands and a point will do for them but they will have much preferred having things sewn up ahead of a trip to France.
The North London outfit have been on the opposite end of late Champions League VAR drama when Raheem Sterling's goal in the dying embers for Manchester City in the quarter-final in April 2019 was disallowed.
Topics: Harry Kane, Antonio Conte, Tottenham Hotspur, Champions League