Switzerland's Wawrinka, who made his debut in 2002 and will celebrate his 41st birthday in March, said last month he wanted to bring the curtain down on his career at the end of the season.
He toiled in the Perth heat to seal a 5-7, 7-6(5), 7-6(5) win over world number 29 Rinderknech, showing the resilience he will hope to take to this month's Australian Open, an event he won in 2014 before enjoying further Grand Slam triumphs at the French and US Opens.
"I'd have loved a quicker win, but no, this is why I keep playing. I'm passionate about the game. I'm always going to push my own limit," Wawrinka told reporters after giving his team a 2-0 lead.
"I've said I've been working hard this off-season. Even if it's my last year, I don't just want to play to play. I want to play to compete and try to win.
"I'm super happy with the performance today, with the win. It was a tough fight, big fight, but I stayed quite positive and really focused on my own discipline during the game.
"I try to find solutions, find the better way of playing. When I got the opportunity to finish, I went for it."
Switzerland went on to seal a 3-0 win in the mixed team event featuring 18 countries.
Wawrinka is currently 157 in the world rankings following a spell of injuries and has not reached a Grand Slam quarter-final since the 2020 Australian Open.
He will require a wildcard to enter the Australian Open, which runs from January 18 to February 1.