Sun won in three sets and will play Anna Blinkova of Russia in the second round.
Sun and Kasatkina had to battle through blustery conditions with the ball “swirling everywhere”, Sun told the WTA afterwards.
The scoreline also swirled around.
Sun went up 4-0 in the first set before Kasatkina reeled off five straight games herself.
Sun saved one set point with a delicate volley and managed to close out the opener.
The 24-year-old Kiwi had to withstand another momentum shift in the second set before regaining control in the third.
Sun won 7-5, 2-6, 6-3.
The World No. 46 had come into Eastbourne with just a 6-15 season record, but found her style rewarded on the lawns of southern England.
“I really enjoy playing on grass,” Sun said in her on-court interview.
“It’s a really unique time of the season.”
It’s an encouraging result for Sun as she prepares for next week’s Wimbledon Championship where she made the quarter-finals last year.
Meanwhile doubles specialist Erin Routliffe has reunited with regular partner Gaby Dabrowski but the top seeds were beaten in their first round match in at a WTA tournament in Germany.
Dabrowski had been out of action for a few weeks with injury.
Routliffe played Roland Garros with Victoria Azarenka and two tournaments since with Lyudmyla Kichenok.
