The all-family final between the 54th-ranked Frenchman Rinderknech and 204th-ranked Vacherot, from Monaco, is one of the tournament's unlikeliest endings to date - the latter's coach and half-brother, Benjamin Balleret, described it as a "fairytale".
It was just the third ATP Masters 1000 final in history to feature two unseeded players.
"I want to thank someone without whom I wouldn't be here - that person is obviously Arthur," said Vacherot as he accepted his trophy.
"It's completely mad, I can't believe it," he added in French.
"It would have been better to have two winners, but a whole family won today.
"What we did this week, it's completely crazy, no one can take it from us."
Elder cousin Rinderknech went ahead in the match first, breaking with a backhand in the third game after three unforced errors from Vacherot.
That was enough for the 30-year-old to claim the set in an otherwise well-matched duel.
Watched on by Roger Federer, the second set continued in much the same vein, with neither player able to make headway early on.
Rinderknech faced a break point in the eighth game and saved with an ace, but failed to convert a subsequent advantage to hold.
He found himself on the brink again after an unforced error when he hit the ball into the net, and Vacherot did not miss his chance this time to force a decider.
The third set went off with a bang, with Vacherot taking his cousin to break point almost immediately to snatch the first game.
The 26-year-old Vacherot looked increasingly dangerous as Rinderknech, seemingly flagging in the humidity, scrambled to save multiple break points in both the third and fifth games.
The Frenchman received treatment on his back after the fifth game, having almost been broken four times.
The partial revival that followed made for some tense rallies that energised the crowd, but Vacherot broke again in the ninth game to seal the title, doubling over in disbelief.
'Two winners'
Rinderknech said after his semi-final that there would be "two winners" on Sunday whatever happened.
The two sat side-by-side, Rinderknech putting his arm around Vacherot's shoulder at one point, as they waited for the prize ceremony to begin.
Both claimed some impressive wins on their path to the final.
Rinderknech took out world number three Alexander Zverev and Daniil Medvedev, while Vacherot ended Novak Djokovic's chance at a fifth title, as well as defeating world number 11 Holger Rune.
According to the ATP website, the Monegasque should rocket from 204 to 40 in the rankings.
Both men were overcome with emotion during the ceremony, in tears, and Rinderknech keeled over and had to be helped into a chair.
"I sweated everything I had, I gave it all, and that's all that matters, and I really enjoyed my time on the court," he said.
