The Dane surrendered the first set after leading 5-1 but recovered to win 6-7(3) 6-3 6-1 as Kuznetsova faded.
Despite taking charge of the match, second seed Wozniacki said she was worried right to the end against the former U.S. Open and French Open champion.
"I was 5-1 up in that first set, so when I was 5-1 up in the third set I was thinking to myself that I really couldn't repeat what happened earlier," she said.
"I served better as the match went on, tried to take the ball a little earlier."
The world number five plays Andrea Petkovic next at the traditional seaside grasscourt tournament after the German beat American CoCo Vandeweghe 6-3 6-4.
Eugenie Bouchard's problems continued as last year's Wimbledon runner-up retired with an abdominal injury when trailing Belinda Bencic 6-4 3-0.
"I was feeling it during the match," Canada's Bouchard told reporters. "It just wasn't smart for me to take a risk, and, you know, potentially be out for a long time.
"It's something I want to kind of take care of right away."
"I'm going to play (Wimbledon) no matter what, even if I'm on one leg," added Bouchard, who has suffered a string of early defeats this year.
British wildcard Johanna Konta continued her surprise run with another shock, this time the world number 146 knocking over Spain's Garbine Muguruza, a day after beating world number eight Ekaterina Makarova.
(Reporting by Martyn Herman; editing by Toby Davis)
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