Elsewhere, Britain’s Marcus Willis also booked his spot in round three, partnering Poland’s Karol Drzewiecki to a 3-6 6-3 7-6 (13-11) victory over Jackson Withrow and John Peers.
After winning the second set, Willis and Drzewiecki saved three break points early in the third and held their serve throughout to force a tie-break.
Withrow and Peers then spurned three match points while Willis and Drzewiecki also lost a match point at 10-9 before converting at the second attempt.
However, Luke Johnson and Dutch partner Sander Arends exited in round two, losing to Argentinian pair Tomas Etcheverry and Camilo Ugo 7-5 7-6 (8-6).
Meanwhile, British interest in the women’s doubles ended when Sonay Kartal and Katie Boulter lost to 12th seeds Zhang Shuai and Ekatarina Alexandrova in three sets.
The British pair came from a set down to send the match to a decider and saved two break points in the second game of the third set.
However, with Kartal and Boulter serving to stay in the match at 5-4, Shuai and Alexandrova took the game to deuce before converting their first match point to close out a 6-4 3-6 6-4 victory and set up a meeting with wildcard pairing Venus Williams and Leylah Fernandez.