Playing in just his second singles match since the Wimbledon final against Novak Djokovic, Kyrgios fired 15 aces - including one serve that clocked in at 218km/h - in a 6-3 6-4 win.
The result doesn't tell the full story of the match, as Paul had Kyrgios under plenty of pressure, forcing the Australian to save four break points.
Kyrgios was up to the task, however, while managing to convert three of the four break points he earned in the match.
While the Australian got up to some of his usual antics, receiving a code violation for ball abuse that led to an argument with the umpire, he also won over the fans with a nice gesture toward an elderly lady in the stands after she was hit in the face by a ball that took a wayward bounce.
He went over to the spectator and handed her one of his towels.
Kyrgios moves on to face Reilly Opelka in the round-of-16 on Friday as he continues his US Open preparations. Opelka advanced with a hard-fought 6-7 (6-8) 6-4 6-4 victory over Denis Kudla.
Kyrgios is chasing his second title in Washington.
Other second-round winners included top seed Andrey Rublev, who beat Jack Draper 6-4 6-2, and third seed Taylor Fritz, who saw off Alexei Popyrin 6-4 6-3.
Sixth seed Denis Shapovalov was knocked out, however, going down 6-2 6-7 (5-7) 6-3 to American J.J. Wolf.