The big-serving Isner blasted 26 aces without a double-fault -- his top serve reached 140 mph -- and also clocked 60 winners (17 unforced errors), to 41 (24 unforced errors) for Giron.
The 2008 French Open champion has struggled to get back to that level but finally seems to be inching closer. She returned to the top 10 this month for the first time in more than five years.
Ivanovic was broken in the first game Tuesday but quickly took control.
The 24-year-old Riske made a breakthrough at last year's U.S. Open, reaching the fourth round after an upset of Petra Kvitova. She reached a career-high ranking of No. 40 this summer.
In other action:
Wimbledon champ and No. 3 seed Petra Kvitova blasted Kristina Mladenovic 6-1, 6-0, needing only 54 minute to end a hot afternoon session at in Arthur Ashe Stadium.
Seventh-seeded Eugenie Bouchard routed Olga Govortsova 6-2, 6-1 in the first round. At her previous major tournament, Bouchard made history at Wimbledon as the first Canadian to reach a Grand Slam final.
Svetlana Kuznetsova lost her first-round match at the for the first time since 2005, the year she was the tournament's defending champion. Kuznetsova, seeded 20th this time, was beaten 3-6, 6-2, 7-6 (3) by 82nd-ranked Marina Erakovic of New Zealand.