The 28-year-old Millman posted a 6-3, 1-6, 6-4, 6-1 victory over the 14th-seeded Kyrgios, who had been plagued by an ailing shoulder injury. Kyrgios requested treatment for his right shoulder early in the third set, but his level of play dropped off significantly as his frustration began to mount.
Kyrgios found himself in an argument with chair umpire Carlos Ramos after being warned for using bad language. Kyrgios disputed Ramos' claim, but the chair umpire said a linesperson reported the use of language.
Millman finished off Kyrgios in two hours, 14 minutes to notch his biggest victory since beating No. 15-ranked Frenchman Richard Gasquet in the 2016 Winston-Salem Open quarterfinals.
Millman advances to play Tunisian Malek Jaziri or Thiago Monteiro of Brazil on Thursday.
Sixth-seeded Austrian Dominic Thiem wrapped up his first-round match in short order, posting a 6-4, 6-1, 6-1 victory over Australian Alex De Minaur. Thiem had won the first two sets and the opening game of the third on Tuesday before the match had been halted by rain.
Also on Wednesday, 18th-seeded Gael Monfils posted a 7-6 (6), 6-3, 6-4 victory over fellow Frenchman Jeremy Chardy and 30th-seeded Frenchman Adrian Mannarino breezed to a 6-2, 6-4, 6-2 triumph over Lithuania's Ricardas Berankis.
Unseeded Stefano Travaglia shocked fellow Italian and 22nd-seeded Fabio Fognini with a 6-4, 7-6 (8), 3-6, 6-0 victory and Argentine Leonardo Mayer notched a 3-6, 6-2, 6-4, 6-2 triumph over 26th-seeded Richard Gasquet.
Bosnia's Damir Dzumhur also secured an upset by bouncing 27th-seeded Argentine Pablo Cuevas 7-5, 7-6 (3), 6-1.
Also emerging victorious on Wednesday were Americans Bjorn Fratangelo, Taylor Fritz and Donald Young, Japan's Yuichi Sugita and Taro Daniel, Ukraine's Alexandr Dolgopolov, Russian Mikhail Youzhny, Spaniard Adrian Menendez-Maceiras and Argentine Guido Pella and Viktor Troicki of Serbia.