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.”
Five days after losing to Sinner in the group stage, Djokovic was in ruthless form from the outset as he lost just two points on serve in winning the opening set 6-3 in 38 minutes.
The world number then raced into a 2-0 lead in the second before Sinner saved three break points in the third game to bring the contest to life.
Roared on by the partisan crowd, Sinner finally got to grips with the Djokovic serve and forged two break points in the sixth game, only for the Serbian to save both and maintain his advantage.
Sinner held serve in a marathon seventh game but, after Djokovic did likewise to lead 5-3, the match ended on an anticlimactic note with a Sinner double fault.
“It’s very special,” Djokovic, who had shared the record of six titles with Roger Federer, said on Amazon Prime. “One of the best seasons I’ve had in my life no doubt.
“To crown it with a win against the hometown hero Jannik, who’s played amazing tennis this week, it’s phenomenal.
“I’m very proud of the performances these last two days against (Carlos) Alcaraz and Sinner, probably the best two players in the world next to me and (Daniil) Medvedev at the moment.
“The way they have been playing I had to step it up, I had to win the matches and not wait for them to hand me the victory and that’s what I’ve done.
“I played tactically different today than in the group stages against Jannik and just overall a phenomenal week.”
Earlier on Sunday, Britain’s Joe Salisbury and American partner Rajeev Ram had successfully defended their doubles title with victory over Marcel Granollers and Horacio Zeballos.
Salisbury and Ram won 6-3 6-4 in 69 minutes to extend their winning streak in Turin to 10 matches.
“I think we’ve got better throughout the week,” Salisbury said. “I think that was our best match, maybe along with the semi-final yesterday.
“I think we’ve served well and not got broken many times. We did that really well and managed to take the few chances we had today. I think we got a little bit of luck as well, but it seems like we get it in this place.”
Djokovic is chasing a record seventh title but again found 20-year-old Rune, who is making his debut at the eight-man event, a troublesome opponent before pulling off a third win in five meetings.
It was past midnight in Turin when Djokovic completed a 7-6 (4) 6-7 (1) 6-3 victory after three hours and four minutes on court.
Rune has fared much better against Djokovic than most of his rivals over the last couple of years, beating him in Paris last autumn and Rome in the spring before a narrow defeat in the French capital a week-and-a-half ago.
The Serbian went on to claim the Masters series title, maintaining his record of not having lost a match since the Wimbledon final.
It was Rune who struck first with a break to lead 3-2 but Djokovic hit straight back and the high-class set went all the way to a tie-break, which the top seed took with a forehand smashed cross-court past his helpless opponent.
Rune reacted well, breaking again to lead 2-0 in the second set, but once more Djokovic found the immediate response, and a strong serve foiled the young Dane when he forced a set point at 4-5.
Rune slumped after reaching the Wimbledon quarter-finals prior to hiring Djokovic’s former coach Boris Becker last month, but there were plenty of moments here to demonstrate his huge talent and fearsome ball-striking.
He has won at least a set against Djokovic in every match they have played, but he had a helping hand in setting up a decider, his rival playing a highly unusual lacklustre tie-break.
Djokovic broke straight away to start the deciding set, only for this time Rune to recover the deficit immediately, prompting a frustrated Djokovic to stamp on two rackets, snapping the frames.
But he broke again to lead 4-2 and this time there was no way back for Rune.
Djokovic told Prime Video: “It took everything. I saw in the first game when he fired shots from the baseline, I knew it was going to be a tough night for me. I thought he played great. I played great in some moments.
“Overall a win is a win. It was a very emotional win and a tough win knowing the significance of tonight’s match. After a really terrible second-set tie-break I think I played a really solid third set.”
Earlier, Italian Jannik Sinner delighted the crowd by defeating Stefanos Tsitsipas in the opening singles match.
Sinner, 22, played as an alternate two years ago but qualified for the first time this season after claiming four ATP Tour titles and rising to world number four. He is one of the favourites to lift the trophy this week, which would be the dream scenario for the home fans, and a 6-4 6-4 victory over Tsitsipas is a big step towards the semi-finals.
