Kerber, seeded second, was making her first appearance in New Haven. She drew a first-round bye.
Vesnina, a 2009 finalist, won the first three games to take control of the first set. She broke serve for the sixth time in the final game of the match. Kerber hit a forehand just wide on match point, then threw her racket in disgust. The call was upheld after a challenge.
Later Tuesday, defending champion Petra Kvitova faces Annika Beck in a match postponed because of rain on Monday night.