Five-time Grand Slam winner Swiatek was on court for the first time since news broke in late November that she served a one-month ban for a doping violation.
But the Pole quickly shook off any nerves in Sydney with a 6-1, 6-0 thrashing of Norway's Malene Helgo, needing just 62 minutes for the demolition job.
"Pleased with everything, honestly. I'm happy for sure with the performance," said the world number two.
"It's not always easy to play for your country, sometimes the pressure is a bit bigger.
"I feel good, I feel happy, happy I can play tennis overall," she added. "I'm just going step by step and we'll see what's next."
The 23-year-old tested positive for the heart medication trimetazidine (TMZ) in an out-of-competition sample in August when she was ranked number one.
However, the International Tennis Integrity Agency (ITIA) accepted that the violation was not intentional and she escaped with a one-month sanction.
While she was in electric form, Greek star Tsitsipas had a day to forget.
He is coming off a mediocre 2024 in which his ranking dropped to its current 11 from a career-high three and was hoping for a confidence-boosting fresh start in Perth.
But he was stunned 6-4, 7-6 (7/0) by 78th-ranked Alexander Shevchenko.
Tried hard
Kazakh world number six and 2022 Wimbledon champion Elena Rybakina then survived a late wobble before burying Greek hopes with a 6-4, 6-3 defeat of Maria Sakkari.
"I'm really happy for the team," said Rybakina, now working with Novak Djokovic's former coach Goran Ivanisevic. "We all tried hard.
"It was a tough match for me today and I'm so happy to be in the quarter-finals."
Rybakina took the first set and led 5-0 in the second, but the former world number three Sakkari won three games in a row to threaten a comeback.
Rybakina came through on her third match point as Sakkari mis-hit an overhead after 85 minutes.
"At 5-0 you have nothing to lose, she played more aggressively and hit some good shots," said Rybakina.
Shevchenko called his defeat of a sluggish Tsitsipas "one of the best" of his career.
"He was not at his best today. But I played really well and found the moment to win that match," he said.
"It will definitely go in my record as one of my best wins."
Defending champions Germany, led by Alexander Zverev, face China in the Perth evening session.
In Sydney, Katie Boulter led Britain to victory over Argentina with all three teams in the group, which also includes hosts Australia, still in contention for the knockout rounds.
World number 24 Boulter took 86 minutes to take down 100th-ranked Nadia Podoroska 6-2, 6-3.
Underdog Billy Harris looked on track to seal the tie for Britain when he went a set up against Tomas Martin Etcheverry.
But the Argentine, who lost heavily to Australia's Alex de Minaur at the weekend, rallied for a gutsy 3-6, 6-3, 6-2 win to send the tie to a deciding mixed doubles.
Etcheverry fronted up again with Maria Carle to take on Boulter and Charles Broom, with the British pair coming out on top 7-6 (7/4), 7-5.
