Sinner and doubles partner Lorenzo Sonego beat the Serbian duo of Djokovic and Miomir Kecmanovic 6-3 6-4 to secure a famous victory that sent the former champions packing and sparked wild celebrations at a heaving Martin Carpena Arena in Spain.
Up next for Filippo Volandri's side, who will be playing in an eighth final and seeking a second trophy, are 28-times champions Australia after Lleyton Hewitt's team eased past giant-killers Finland on Friday.
Sinner earlier saved three match points to stun Djokovic 6-2, 2-6, 7-5 in an extraordinary singles match to help Italy draw level with Serbia at 1-1 after Kecmanovic had put the 2010 champions ahead by beating Lorenzo Musetti 6-7(7), 6-2, 6-1.
Sinner was facing Djokovic for the third time in 11 days and the world number four, who beat the top-ranked Serbian early in the ATP Finals before losing to him in the title clash, made a quick start to ease through the opening set with two breaks.
Sinner, who had sparked Italy's comeback in their quarter-final against the Netherlands, took his foot off the gas in the next set to allow Djokovic back in but kept chipping away in the hope of sealing a second win over him in six meetings.
He saved three matchpoints from 0-40 at 4-5 in the decider and then broke Djokovic for a 6-5 lead before holding his nerve to make a forehand pass and pull off one of the most remarkable wins of his career amid deafening cheers.
"It was for sure the game-changer today," Sinner said of his singles heroics at 4-5.
"I just tried to push in every single point and the 0-40 game helped the confidence and also after I broke him. It's all part of tennis.
"Obviously playing doubles in the decider of a Davis Cup tie is not easy. There's a lot of pressure, I think we both handled it really well. We are a very complete team and each one of us is really happy to be here.
"Tomorrow we'll try our best. Let's see what's coming."
Defeat was a bitter pill for Djokovic, the winner of three of the four Grand Slams in a stellar season, as he lost his first Davis Cup singles match since the semi-final in 2011 when he retired against Argentina's Juan Martin del Potro.
It was only the fourth time Djokovic had lost a tour-level match after having a matchpoint and Sinner also became the first player to beat the 24-times Grand Slam champion twice in singles in the same season since Daniil Medvedev in 2019.
Kecmanovic had earlier rallied from a set down to power past Musetti and leave Serbia one win away from their third final in the elite men's team competition and first since 2013.
Musetti made a slow start against the high-flying Kecmanovic and narrowly avoided going down a double break, before the world number 27 found his range to level the first set at 5-5 and come from behind again in the tiebreak to clinch it.
Kecmanovic's level barely dropped, as the world number 55 breezed through the next set and broke twice in the third for a 4-0 lead, which was enough for the 24-year-old to see off Musetti who was battling a thigh issue.
But Kecmanovic's level barely dropped following the setback, as the world number 55 breezed through the second set and broke twice in the third for a 4-0 lead, which was enough for the 24-year-old to see off Musetti who was battling a thigh issue.
