Wawrinka, whose ranking has slipped to 148 on the back of a series of injuries in recent years, defeated Bublik 6-3 7-6 (7-3) on Friday night to give Switzerland an unassailable 3-0 lead.
Bublik put up a good fight, but the world No.37 wasn't able to snare the win that would have kept Kazakhstan's hopes of winning the tie alive.
"I was super happy when they announced this United Cup, to have the chance to play for the Swiss with my teammates and everybody and to play here in Brisbane," Wawrinka said.
"Tonight was a great level.
"I'm super happy with the way I was playing. I've been working really hard to be back at a better level and I'm happy with the performance today."
An injury retirement assisted the United States on their way to a 4-1 win over the Czech Republic in Sydney.
Italy also beat Brazil 3-2 in their best-of-five-match tie thanks to Lucia Bronzetti and Matteo Berrettini winning their singles ties at Pat Rafter Arena in Brisbane.
World No.19 Frances Tiafoe won the first set 6-3 for the United States against Czech 22-year-old Tomas Machac, but Machac was leading 4-2 in the second set when he rolled his ankle and was forced to retire from the match.
Tiafoe said Machac was playing extremely well when he went down, and he felt for his opponent.
"We were in the midst of a battle," Tiafoe told the Nine Network.
"It sucks that I got over the line this way. You don't want to see that. Hopefully he can get right for the Australian Open."
Tiafoe said that he hoped the US could "do something special" in the rest of the United Cup.
The Czech Republic had earlier stayed in the tie courtesy of Petra Kvitova's 7-6 (8-6) 6-4 win over world No.3 Jessica Pegula. The US had a 2-0 lead after the first day's play.
Pegula was in control when leading 5-1 in the first set tiebreaker but Kvitova fought back brilliantly
The world No.16 broke Pegula early in the second set and did not take her foot off the throat.
United States pair Pegula and Taylor Fritz beat Marie Bouzkova and Jiri Lehecka 2-6 6-3 and 10-7 in a match tiebreak in the mixed doubles to finish off the tie.
In Brisbane, the power game of Italy's Matteo Berrettini proved decisive in his 6-4 7-6 (9-7) win over Brazilian Thiago Monteiro.
The win gave Italy a 2-1 lead in their tie after both countries won matches on day one.
World No.16 Berrettini will play world No.3 Casper Ruud on Tuesday in the Italy-Norway tie, a match that could well prove decisive in which nation goes through.
Ruud leads 4-2 in their head-to-head clashes.
"Casper is one of the best tennis players in the world and has had an unbelievable season," Berrettini said.
"We always have great battles. It is my first time playing him for Italy and that is going to be extra motivation."
Bronzetti put the tie out of Brazil's reach when she blew Laura Pigossi off the court with a 6-0 6-2 win.
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