Unseeded Safiullin beat 13th seed Tiafoe 5-7, 7-5, 7-6 in a three-hour contest where the American initially lost his cool when he received a time violation while serving with the score tied at 5-5 during the final set tiebreak.
"No, no, I tossed the ball up... I was ready to serve. Dude, that's the rule," Tiafoe said repeatedly as he walked towards the net while trying to convince the Ecuadorian chair umpire Jimmy Pinoargote.
"I'm not buying it, it's the second serve," the umpire said in response, putting an end to the discussion by announcing "second serve" on the microphone. Tiafoe went on to lose the point and eventually the match.
After shaking Safiullin's hand at the net, Tiafoe directed his anger at Pinoargote, repeatedly hurling expletives at the umpire as he walked back to his seat, as the small crowd of fans who had stayed behind laughed at his antics.
The ATP did not immediately comment on the incident but the rule book says the 26-year-old can expect to be fined, with the amount going up to $60,000 for each violation at Masters 1000 tournaments.
Tiafoe later posted an apology on Instagram for the way he acted.
"That is not who I am and not how I ever want to treat people. I let my frustration in the heat of the moment get the best of me and I'm extremely disappointed with how I handled the situation," Tiafoe said.
"That's not acceptable behaviour and I want to apologize to the umpire, the tournament, and the fans."
Tiafoe, who is ranked number 17 in the world, had enjoyed some late-season form where he reached the finals of the Citi Open and the Cincinnati Open while he also advanced to the semi-finals of the US Open.