During prolonged exchanges between the pair, Kyrgios was heard saying "I don't care" and then told the umpire: "You have no right to tell me it's poor".
The Aussie looked solid in the opening set as Klahn - ranked 104 in the world - didn't look overly threatening to Kyrgios' charge.
Last night, the 23-year-old was dumped out of the Shanghai Masters, following a clash with an umpire who deemed his efforts to be 'borderline'.
The Croatian saved two break points at 3-3 in the second set and claimed three of the first four games in the decider.
Three games later, Kyrgios smashed an ace and turned to Dumusois to ask "was that borderline poor?" before the French official told him "that's enough".
As Klahn accepted the plaudits from the crowd, Kyrgios left the court using his mobile phone.
He was later fined $10,000 for unsportsmanlike conduct.
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Federer has talked up Kyrgios in the past but the Australian still seems prone to controversy despite spending years on the ATP Tour. On that day, he belted two balls out of the stadium, and walked out midway through the match.
Kyrgios has a chequered history at the Shanghai Masters after quitting mid-match against Steve Johnson in the first round past year and being accused of tanking in a second-round loss to Mischa Zverev in 2016.
Deposed this week as Australian No 1 by Alex de Minaur, Kyrgios argued with umpire Damien Dumusois after the Frenchman questioned Kyrgios' effort.
The Swede climbing down from his chair in NY to have a lengthy chat with Kyrgios when he was showing little effort as he trailed by a set and 3-0 down against Pierre-Hugues Herbert.
Sam Querrey, Mackenzie McDonald, Bradley Klahn and Taylor Fritz all posted wins in the first round of the tournament, while Frances Tiafoe lost his match. A press conference for the Argentine on Tuesday was cancelled at the last moment, however, which suggests that he could still be unwell.Top seed and holder Federer starts his campaign on Wednesday against Russia's Daniil Medvedev.
Wawrinka, who is trying to discover his form following knee surgery, took the opener 6-4 but 13th seed Coric roared back and won his 32nd match of the season.