Matches at the UTS, co-owned by Patrick Mouratoglou, the long-time coach of Serena Williams, consist of four 10-minute quarters, with a two-minute break between them, and the player with most points win the quarter.
De Minaur celebrates winning UTS 3
Moutet, ranked 75th in the world, saw a 2-0 lead in the match slip and lost his cool in the fourth quarter, accusing his opponent's father and coach, Apostolos, for being disrespectful by talking when he was getting ready to serve.
Corentin Moutet tries but fails to showboat
The players got into a heated on-court discussion as Apostolos watched on before the umpire intervened and asked the players to resume play.
"I won't speak about Stefanos, because he's a good guy. But it's just (his) father is stupid, everyone thinks he's stupid," Moutet told commentators during the break. "He's speaking when I'm serving, all the time. It's not respectful."
The argument did not seem to have bothered Tsitsipas too much as he squared the match at 2-2 and then won it in sudden death.
"I had experience with this in the past. I don't want to say more, but I don't see why there should be a problem," said men's world number six Tsitsipas.
My father is trying to encourage me before the serve and he's not really interrupting. My opponent makes a big deal out of it.
Tsitsipas, Richard Gasquet, Matteo Berrettini, and David Goffin have booked their spots in the semi-finals of the tournament, which is being held without fans at Mouratoglou's academy in Nice, France.
UTS highlights: Richard Gasquet gets better of Alexei Popyrin
World number three Dominic Thiem was the highest-ranked player at the tournament before the Austrian headed off to play in the exhibition event he is organising in Kitzbuhel.
Highlights: De Minaur beats Gasquet to win UTS 3
'The Demon' Alex de Minaur wins Ultimate Tennis Showdown 3