The former world number three dispatched Shintaro Mochizuki 6-3, 6-4 as he played his first match in almost four months after a recurring back injury forced him to take a break from the sport.
"I've had a lot of uncertainty, I didn't know if I could compete," Tsitsipas said. "But to play at this level is something I'm very grateful for.
"I'm healthy and that's the most important thing in the world. I hope this tournament can give me some confidence before the Australian Open," added the 27-year-old two-time Grand Slam finalist.
Teammate Maria Sakkari began the tie with a 6-4, 6-2 defeat of Naomi Osaka.
Japan's former world number one is suffering from a head cold and played far from her best in Perth.
"I was not operating at the per cent I would want, I did not play amazing," the four-time Grand Slam champion said.
"Honestly, it was not a bad first match for what it was. I'm thankful I have another to play. I need to not be afraid of making mistakes."
Tsitsipas and Sakkari will team up for Greece's dead-rubber mixed singles tie later on Friday.
Earlier, Sebastian Baez and Solana Sierra led Argentina to a 3-0 defeat of Spain.
World number 45 Baez got Argentina on the scoreboard with a 6-4, 6-4 victory over Jaume Munar, earning a surprise win on hard court after just three victories in nine matches on the surface last season.
The South Americans clinched the win when 66th-ranked tournament debutante Sierra held her nerve for a 6-4, 5-7, 6-0 defeat of Jessica Bouzas Maneiro.
The 21-year-old, who reached the fourth round at Wimbledon last year, said: "I knew I had to be tough. I'm super-happy with my level."
Argentina then won the mixed doubles rubber in straight sets.
Ties at the United Cup comprise one men's and one women's singles and a mixed doubles, with group winners in each host city - Perth and Sydney - advancing to the quarter-finals along with the best runners-up.