The American rookie was able to take advantage of the unexpectedly good form of the Williams at the Dutch GP venue, which also propelled his team-mate Alex Albon to fourth on the grid.
Sargeant got through a wet Q2 in an encouraging 10th place but then crashed heavily on slicks early in the final segment of qualifying.
He thus finished last in the session and will start Sunday’s race from 10th.
“It's just tough, fine margins in those conditions,” he said when asked by Autosport about his mixed fortunes.
“Last thing I ever want to do is leave the team with a boatload of damage, but I'm doing my best to deliver good results.
“I think there's been so many positives this weekend. Yesterday in the dry I felt like I was really pretty much right there. I think the long-run pace was really good. We've had the car in a great window.
“Even Q1, Q2, I missed a little bit of pace today in the wet. But I think the biggest positive for me is delivering laps when I needed to. And that's something I've lacked this year. And to be able to do that has been really nice today. But it's all just shadowed by a millimetre mistake.”
Source: Autosport