Moments after Djokovic clinched victory, Safiullin served out to win a final-set tie-break against American 13th seed Frances Tiafoe.
Tiafoe, 26, reacted angrily towards chair umpire Jimmy Pinoargote after losing 5-7 7-5 7-6 (7-5), launching a flurry of expletives in the Ecuadorian official’s direction.
Tiafoe could face a fine of up to $60,000 (ÂŁ46,000) for the outburst, classified as a verbal abuse offence in the ATP rules.
The incident may be escalated if tournament officials feel it was ‘flagrant and particularly injurious to the success of a tournament, or singularly egregious’.
If Tiafoe’s actions are considered an ‘offence of aggravated behaviour’ or ‘conduct contrary to the integrity of the game’, the two-time US Open semi-finalist could face a larger fine.
Tiafoe’s outburst came after a defeat that turned on the American being given a time violation at 5-5 in the tie-break.
He claimed he tossed the ball up to serve, but Pinoargote disagreed it was a legitimate throw intended to start the point and penalised him.
Forced to start with a second serve, Tiafoe lost the point after an exciting all-court exchange for 6-5 to Safiullin, who clinched victory at the first attempt.
Meanwhile, German second seed Alexander Zverev took his eighth match point to beat Tallon Griekspoor of the Netherlands, while other top-10 seeds Taylor Fritz, Grigor Dimitrov and Stefanos Tsitsipas also progressed on Tuesday.
Tsitsipas beat France’s Alexandre Muller to set up a fourth-round meeting with Russian fifth seed Daniil Medvedev, relaunching a rivalry that has provided drama in the past.