Katie Boulter number one England recovered from the set to defeat Irina-Camelia Begu in the second half in India Wells.
The Romanian player won the first set in a tie breaker but Boulter then took over to win 6-7 (2-7) 6-3 6-0 in California.
Boulter, 28, played only his third tournament this year and had a bye in the first round while begu, ranked 74 in the world, defeating Ann Li from the United States.
The British woman will face a much harder test in the third round when she faces Elena Rybakina from Kazakhstan, seventh seed.
Boulter has fallen to 38 in the world ranking that has not played since eliminated from The second half opens Australia in January.
