Vesnina had lost all three of her previous encounters with Kerber, but this time she won the first set comfortably and after going down a break at 3-2 in the second, won four of the next five games for a 62 64 victory.
"She's a very tough player, can win on any surface and is a fighter, so it was important for me to get early confidence by winning the first set," Vesnina said. "The second set was up and down with a lot of breaks, but at the key moments I served well."
Vesnina's defeat of World No.10 Kerber was her sixth career Top 10 win and second this year.
"Going against a Top 10 player is always tough because they have a lot of confidence," Vesnina said. "It was important for me to play my game, take my chances, be consistent and be aggressive."
Vesnina has had success at New Haven in the past, most notably with a runner-up showing in 2009.
"I have great memories here from 2009," Vesnina said. "I feel really good about this tournament, the atmosphere, the courts. Some players feel certain tournaments are their place. That's how I feel about this tournament."
Kerber said she will be right back on court Wednesday practicing for next week's US Open.
"I tried to fight, but she was playing well and I couldn't find my rhythm," Kerber said. "Sometimes you have days like this. I will just try to take the positives from the match and focus on the next event."
"I feel good today," Zakopalova said. "I played better than yesterday. I was focused from the first point to the last. The first set was very tough. I was 3-1 down, so winning that gave me confidence for the rest of the way."
Zakopalova said taking on up-and-comers like the 19-year-old Puig is always a challenge.
"She fights for every point," Zakopalova said. "She has nothing to lose. It's very dangerous to play against young girls like that."
Also in daytime action, No.3 seed and defending champion Petra Kvitova got past Annika Beck, 46 63 63, in the last match of the first round. Kvitova was down a set and a break, but converted on six of eight break point chances in the second and third sets en route to victory.