The Romanian won the first set in a tie-break but Boulter then took charge to win 6-7 (2-7) 6-3 6-0 in California.

Boulter, 28, is playing just her third tournament of the year and had a bye in the first round while Begu, ranked 74 in the world, beat Ann Li of the USA.

The Englishwoman will face a much sterner test in the third round when she plays Kazakhstan’s Elena Rybakina, with the seventh seed having beaten Suzan Lamens of the Netherlands 6-3 6-3.

Boulter has dropped to 38 in the world rankings having not played since January’s Australian Open because of a foot injury.

“Two weeks ago I was in a boot, I was not really playing tennis at all,” she told BBC Sport.

“I was trying to keep my eye in by sitting on a box and hitting some volleys but that’s the extent of where we’ve been out on the tennis court.

“To get through today it really shows how much I have fought to get through these last few weeks and how much I have been pushing myself to get back out here. It feels worth it now that at least I got one win under the belt. We’ll see how the foot reacts and go from there.”

Elsewhere, Tunisia’s former world number two Ons Jabeur was beaten 6-3 6-1 by Ukraine’s Dayana Yastremska, while there was victory for Yastremska’s compatriot Marta Kostyuk.

The 18th seed beat American Robin Montgomery 6-1 6-3.

Poland’s second seed Iga Swiatek faces France’s Caroline Garcia later on day three of action, before fourth seed and home favourite Jessica Pegula plays another Pole, Magda Linette.