Spurs were stunned 3-2 by the relegation battlers, with Sanchez having a hand in two of the Cherries' goals before being substituted after just 23 minutes on the pitch.
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Heung-min Son gave Tottenham a perfect start to the game with the opener after just 13 minutes with a deflected shot, but it soon unravelled for the hosts.
Matias Vina then pulled Bournemouth level with a lovely chipped finish after a shambolic sequence from Sanchez, whose every touch of the ball was booed by a section of home supporters.
The centre-back got the ball tangled in his legs before a poor pass out from the back, which was pounced upon by the visitors and he then failed to track his man back as Vina ran through on goal to score.
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Sanchez then provided the assist for Dominic Solanke to put Bournemouth in front, with defender inadvertently poking the ball into the striker's path as he slotted past Hugo Lloris.
Sanchez had only come onto the pitch in the 35th minute after an injury to Clement Lenglet forced Spurs into a change.
But he was hauled off with 58 minutes on the clock, moments after Solanke's goal, to a mixture of more boos and ironic cheers, with interim manager Cristian Stellini accused of 'burying' the player with his decision.
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He was replaced by Arnaut Danjuma, who appeared to have rescued a point for Spurs with a goal against his former club.
But Bournemouth refused to back down and won the game in stoppage-time thanks to a first goal for the club from January signing Dango Ouattara.
"Stellini has absolutely buried Sanchez there," said talkSPORT co-commentator Perry Groves, speaking live from the Tottenham Hotspur Stadium.
"He was involved in Bournemouth's first goal and he could have done better for the second.
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"I didn't think he'd been that bad to get the hook. That is the worst thing that can happen to you has a player, when you've only been on for 25 or 30 minutes.
"To be honest, I'm looking at the body language of all the Spurs players, and there's nobody berating and shouting at their teammates to get them going. They've all just turned around, hands on hips, almost like acceptance.
"You need big players to come out, take responsibility and inspire the other players - but I'm not seeing that from Tottenham."
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Although Groves thought it was harsh on Sanchez, Spurs supporters made their feelings about the centre-back loud and clear, with former midfielder Jamie O'Hara adding his reaction on social media.
The talkSPORT pundit wrote on Twitter: "Spurs, wow. Sanchez, wow. Seriously, what am I watching?"
White Hart Lane hero Michael Dawson was also watching the game, and was disappointed by the reaction of Spurs supporters towards the defender.
"He was brought on late in the first-half, and it wasn't even his fault for the first goal - he passes it to Pedro Porro, Porro loses the ball and the goal then happens," the former Spurs centre-back and captain said on Sky Sports.
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"The second goal, the ball ricochets and goes to the feet of Solanke.
"However, Stellini has made the decision to bring him off again, no problem with that, but what I don't like is when your own fans boo you.
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"I feel for Sanchez because that's awful for a player, his confidence looks shot.
"He'll be hurting, it's not nice to see. A horrible day for him today."
The defeat is a hammer blow to Tottenham's top-four chances. Spurs sit in fifth place, three points behind Man United in fourth, but the Red Devils have two games in hand.
For Bournemouth, the memorable victory is a huge boost to their survival hopes with the Cherries now six points clear of the bottom-three.