Bates, who will now meet the 1991 Wimbledon champion, Michael Stich, in the second round, said: 'I changed the position of where I was standing to receive his service midway through the second set and his serve seemed to go off after that.'
Kuhnen, ranked 87th in the world, served 13 aces but also made 14 double-faults and Bates was able to coast through the final set.
Britain's No 2, Chris Wilkinson, was even more impressive, recovering from one set down and 5-1 down in the second-set tie-break to beat the American Jared Palmer 2-6, 7-6, 6-3.
Wilkinson, who was a wild-card entry to the tournament, is rewarded with a second-round tie with Goran Ivanisevic, who lost to Andre Agassi in last year's Wimbledon final. 'It should be interesting,' Wilkinson drily remarked on the prospect.
He added: 'I was really struggling in the first set but I thought that if I stuck it out I might come out of the nightmare. It's nice to win your first grass-court match of the year - I've not played on it since the Davis Cup tie against India last September.'
Shirli-Ann Siddall, of Dorset, lost in the first round of the DFS Classic in Birmingham, beaten by the Australian Michelle Jaggard-Lai after a tense two-and-a-half hour battle. The 18-year-old, who reached the third round last year, lost 7-6, 6-7, 6-2.
'She came out and played four good games and I couldn't get my first serve in,' Siddall said.
Jo Durie, forced to withdraw from the tournament after a knee operation three weeks ago, is striving to be fit enough for the Volkswagen Cup at Eastbourne next week but could miss it and Wimbledon.