Only 72 players managed to complete their round in gusting winds and heavy rain at Spijk before the course became flooded and play was suspended.
In that context the five-under-par 66s shot by Wiesberger and Finch, the latter signing for his lowest European Tour round in two years just before play was halted, were impressive.
Wiesberger carded seven birdies to Finch's six but had two bogeys as opposed to the Englishman's one.
"The conditions were really tough out there and although I gave away a couple of easy shots I am really happy with the score and the way I played today," said the Austrian.
"I putted nicely today and controlled the ball flight well. I think I only missed three or four greens which was pretty good in these conditions.
"I have been playing well recently but maybe not getting the results I feel I should have been getting so hopefully I can change that soon."
Finch lost his card in 2015 and made his first cut for 20 months in Denmark last month.
He was pleased to maintain some momentum, making birdies at his first two holes and then four in succession on the back nine.
"It was important to get off to a good start today because when you are playing on conditions like this you know it's going to be a battle so to start with two birdies was huge -- it felt like I had a bit of credit in the bank," said the 40-year-old.
"It's been a while since I have been at the top of a leaderboard, to be honest.
"I missed last year through injury and haven't really got it going since I came back but today was very encouraging and I hope to be able to keep that going for the next few days."
The pair lead by one from Sweden's Joakim Lagergren and China's Ashun Wu with the first round set to resume at 8am local time on Friday.