Radwanska suffered a surprise opening round defeat last week in Birmingham, but against Govortsova never looked in danger of another early exit. After an early exchange of breaks, Radwanska regained her composure in spectacular style, reeling off 11 straight games to wrap up a 62 60 win.
"I like grass so I always look forward to this time of year. I have lots of good memories from here so, for sure, I'm feeling confident," Radwanska said. "I played well today and was pleased to get a win after losing early in Birmingham.
"I like the club here and the people are really nice so I hope I will be staying for a while longer!"
A succession of health problems have led to Krajicek, who won the title here in 2007, playing just two tournaments over the past 12 months, yet against Sílvia Soler-Espinosa she looked sharp, hitting 11 aces on her way to a 75 64 win.
Bertens, on the other hand, looked far less assured on the grass, slipping to a 61 62 defeat to Anabel Medina Garrigues.
"I'm really happy to win the first round because grass probably isn't my best surface," Medina Garrigues said. "I've been here five or six times in the past and I like playing here.
"Sometimes it is tough playing the first match, but today it was great and the court was like a carpet. Hopefully I can win a few more matches to help me get ready for Wimbledon."