Broady had to dig deep for a 7-6 (9/7) 6-4 success against the Californian teenager ranked 69 places above her at 54 in the world.
A hard-fought first set lasted more than 53 minutes in which both players were broken once, but big-serving Broady’s 11 aces were decisive as she edged in front via a tie-break.
The 27-year-old from Stockport then broke again to go 2-1 up in the second set, and never relinquished the advantage – finishing with 17 aces to her opponent’s one.
Broady will play either Hungary’s Timea Babos or a qualifier in round two.
