Anne Keothavong lost on a final set tie-break to New Zealand's Marina Erakovic in the Texas Open first round.
The British number two was beaten 6-1 5-7 7-6 (11-9) by the world number 54.
Keothavong, 28, ranked 80 in the world, battled back after losing the opening set and was a break up in the final set only to lose on a tie-break.
Erakovic and British number one Heather Watson won their first round match in the doubles against Elizabeth Lumpkin and Yasmin Schnack.
They beat the Americans 6-2 2-6 10-8 to reach the second round.
Emily Webley-Smith was beaten by Croatian qualifier Mirjana Lucic 6-1 6-2.
Britain's number 11 was given a late call-up as a lucky loser following Angelique Kerber's withdrawal with a shoulder injury but was comprehensively beaten by the world number 97.