The American, who was outplayed for large parts of their second ATP Head2Head meeting, hit seven double faults and twice came within two points of losing to Kokkinakis, who struck 23 aces. But a strong performance in the deciding-set tie-break helped the 28-year-old to just his fifth match win of the year.
Kudla dug himself out of danger from 1-1, 0/40 in the second set, and saved three break points from 15/40 at 0-1 in the decider against Kokkinakis, the 2017 finalist (l. to Querrey), for victory in three hours and 11 minutes.
World No. 107 Kudla, who reached the Wimbledon third round (l. to Djokovic), will next challenge a fellow American — eighth seed Mackenzie McDonald or qualifier Ernesto Escobedo — in the second round.
Elsewhere on day one, sixth-seeded American Steve Johnson fired 15 aces to overcome Gerardo Lopez Villasenor, a Mexican wild card, 7-6(4), 6-2 in one hour and 41 minutes. Johnson awaits the winner between Japan’s Yasutaka Uchiyama and American qualifier Alexander Sarkissian.
Alex Bolt lost the first seven games of the match against seventh seed Andreas Seppi of Italy before the Australian battled back to win 0-6, 6-2, 6-3 in one hour and 36 minutes. He will next play Ecuador’s Emilio Gomez or Colombian qualifier Nicolas Mejia.