France's Gonnet and Japan's Teshima enjoyed bogey-free rounds in calm conditions at Kennemer Golf and Country Club.
Gonnet was coming off a second-place finish at the Scandinavia Masters.
'Last week was very good and to follow that with a low round is very positive,' Gonnet said. 'But my goal is to get a victory and there is a long way to go.'
Teshima hoped he would be more consistent than on previous occasions when he couldn't take advantage of excellent starts.
'I shot 64 in Italy (at the Italian Open), 8 under, but then followed up with a 77 and missed the cut by one,' Teshima said.
Among the seven golfers that are one stroke behind were former U.S. Open champion Michael Campbell, 2004 winner David Lynn, Sweden's Alexander Noren and Britain's Steve Webster.
Teenage newcomer Stefan Langer of Germany hit a 28-over 98, 31 strokes behind his father, Bernhard Langer. At 67, the three-time Dutch Open winner was three strokes behind Gonnet and Teshima.
Defending champion Simon Dyson started with a 3-under 67.