Rashitov, considered relatively new to the international stage, made a stunning comeback early in the first round before taking a five-advantage into the second.
Defending world champion Sinden had his hands full with Rashitov finding gaps to land shots to the trunk. He managed to fight his way back into contention, getting within four points going into the third and final round.
I believed only in gold, I trained only for gold.
The momentum seemed to swing in Sinden's favour in the third round and he levelled the scores with a combination head and trunk kick.
Sinden got his nose in front for the first time since the first round and looked set to claim a famous victory as the clock ran down.
But the tenacious Rashitov fought back valiantly, landing a four-point turning body kick inside the final 15 seconds for a 34-29 victory to claim Uzbekistan's first-ever medal in taekwondo.
"It's great, the best emotion ever. Nothing can beat winning gold," Rashitov said.
"I believed only in gold, I trained only for gold."
Meanwhile, China's ZHAO Shuai beat South Korean legend LEE Dae-Hoon 17-15 for top honours in one of the bronze-medal matches.
Two-time world champion Zhao, who won Olympic gold in the lighter -58kg category in Rio 2016, demonstrated his class to add the bronze medal in the heavier class.
"After the fight, I sat on the mat to take in the moment and feel the emotion," he said. "I could not get gold because I didn't perform in the semi-final, but I got bronze. "I controlled the pace well, and I took my chance."
Earlier, Hakan Recber earned Turkey's first medal of the Tokyo 2020 Games after beating Nedzad Husic of Bosnia and Herzegovina 22-13 in their bronze-medal bout.
"I am a little bit of a superstar, but my coach is Servet Tazegut (Turkish London 2012 champion), he is the real legend. He is next level," an elated Recber said. "The plan was always to win the gold, but bronze in the Olympic Games is a great achievement. I am not unhappy with bronze."
The taekwondo competition continues on 26 July with the quarters, semis and finals in the women's -67kg and the men's -80kg category from the busy Makuhari Messe Hall A.