It was the first encounter between the Spaniard and Russian, with the latter hoping to bounce back from Monday’s loss to compatriot Daniil Medvedev.
Instead he found himself pinned back by world number two Alcaraz, who never faced a break point and kept his hopes of advancing from the the Red Group alive with his first win at the year-end event after missing the last edition with an abdominal injury.
Alcaraz’s critical break came in the 11th game of the first set, during which he dropped just one point on his first serve and soon his opponent began to unravel.
Rublev dropped his serve to start the second set and could not rein in his reaction as he slammed his racquet against his knee with such force he drew blood, mopping it up with a towel at his chair before returning to the court.
It was all too much to overcome as Alcaraz, who finished with 21 winners to 11 unforced errors, sealed the 74-minute victory with his first match point.
The 20-year-old, who improved to 1-1 following his opening loss to Alexander Zverev, will face Medvedev to conclude the group stage on Friday while Rublev will take on Zverev.
Alcaraz told the ATP website: “It was a totally different match and level from me. This is the level I have to play if I want to give myself a chance in this amazing tournament.
“Yesterday was a good day for me in practise to find the level I needed to show today and I think I did pretty well. I am very happy with my level.”
The 22-year-old Italian won a three-hour marathon 7-5 6-7 (5) 7-6 (2) in a match of high tension and tremendous quality.
Defending champion Djokovic next faces Poland’s Hubert Hurkacz on Thursday in his final group match as he bids to reach the semi-finals.
In front of a raucous home crowd, Sinner grabbed the crucial break in the 11th game, despite finding himself 40-0 down, and then held to love to take the first set.
Djokovic, on a 19-match winning streak, took the second set to a tie-break and was twice a mini-break down before levelling the match, cupping his ear to the spectators.
World number four Sinner then played a stunning return game, breaking Djokovic to 15 with a punishing forehand to move 4-2 up in the third.
But with two hours and 40 minutes on the clock, Djokovic finally broke his young opponent for the first time in the match.
At 5-6 Djokovic began conducting the jeering crowd from his seat at the changeover.
The six-time ATP Finals champion had won 30 tie-breaks this season but number 31 proved elusive as Sinner moved 5-0 up before sealing a statement win with a smash.
“I feel I’m a bit more confident in certain moments but I still have to learn many things,” he said on Amazon Prime.
“I think I was really brave and intelligent, especially in the third set. I think we both played really well.
“It means a lot to me. When you win against the world number one who won 24 grand slams it’s up at the top.”
The afternoon match ended prematurely when Stefanos Tsitsipas retired after just 15 minutes, handing Holger Rune his first win.
Denmark’s Rune, 20, was leading 2-1 when Greek world number six Tsitsipas pulled out due to a back injury.
Tsitsipas was forced to withdraw from the tournament and was replaced by Hurkacz.
“Unfortunately, I felt terrible on the court. I did what I could do in the best possible way to be ready and fit for this match, but it didn’t work out for me,” Tsitsipas, the 2019 champion, said in his press conference.
“It kills me not to be able to finish this tournament, the one that I’ve prepped for for so long.”
