VIDEO: Poland v SA, Davis Cup Day 1 highlights
De Voest produced a memorable display against Kubot, ranked 91st in the ATP singles rankings.
De Voest, at 227th in the rankings, used all his experience to overcome his much fancied opponent on home turf.
"I played a great match today," said De Voest after the rubber.
"I've been playing really well over the last month. I felt confident coming into this match. I knew how to play today. It was a good match."
De Voest said he knew Kubot's game well coming into the tie.
"Lukasz is a great player. We played doubles together some time ago. We've had a few matches in singles too. I've beaten him a couple of times."
South Africa would head to the doubles rubber on Saturday with De Voest expected to partner Ruan Roelofse against Mariusz Fyrstenberg and Marcin Matkowski.
Earlier, South Africa's number two Jean Andersen lost in straight sets 6-4, 6-3, 6-3 to Polish number one Jerzy Janowicz. Janowicz, ranked 24th in the world, was a heavy favourite for the clash, but had his troubles against the South African, ranked at 758th.
In the end, though, the quality of Janowicz was too much for Andersen as South Africa fell behind early in the tie.
"It was a really tough match. At the beginning I was having trouble returning," Anderson said.
"I tried to predict his serves. Obviously I'm disappointed about losing but quite happy with my game. I created chances but unfortunately couldn't capitalise them. He came up with his huge serve whenever it was 15-40 or 30-40. So that was tough," said Andersen.