Clarke, who shared the second-round lead with Englands Robert Rock and Swedens Alexander Noren, had birdies at Nos. 4, 6 and 7 before a bogey at No. 8.
But Clarke was back in contention after birdies on Nos. 12-13 got him to 12-under 198 and boosted his bid to get a Ryder Cup wild card on Nick Faldos European team.
I came here to try to show Nick I have a bit of game and if I play well I have a great chance, Clarke said.
The KLM Open is one of the last chances ' along with next weekends Johnnie Walker Championship in Scotland ' for players to try to earn a Ryder Cup spot.
I can still play better, Clarke said. This week has been good in that I have hit a lot of good shots and made a lot of chances.
Swedens Stenson shot a 68, while Englishman John Bickertons 66 put him third, four strokes behind Clarke.
Noren was tied for sixth after a bogey at No. 8, but had three birdies in the first five holes on the back nine to finish with a 72.