But there was no joy for former world No 1 Andy Murray, who suffered a 7-6 (7-3), 6-1 loss to fifth seed Andrey Rublev to exit the event where he lost the 2009 final to Rafael Nadal.
Australian Open champion Sinner dominated Thanasi Kokkinakis 6-3, 6-0 while women’s world No 1 Swiatek did the same to American Danielle Collins.
Italy’s Sinner, seeded third, backed up his debut Grand Slam title in Melbourne with a victory in the ATP 500 level tournament at Rotterdam last month.
He remains undefeated this season and completed a 13th consecutive match victory while improving to 4-0 over Kokkinakis.
Sinner has won his last 15 meetings with Aussie opponents, last losing to one three years ago in Toronto.
Swiatek, the 2022 Indian Wells champion and last year’s Roland Garros winner who will start her 94th week at the top of the WTA rankings on Monday, broke Collins four times and wrapped up victory on her second match point.
“I’m happy I started the tournament well,” the Polish star said. “First rounds are never easy.”
“Danielle hits the ball hard, I’m happy I went through. I wanted to be ready for anything, I didn’t give her a chance, the small differences matter a lot.”
Reigning Wimbledon champion Marketa Vondrousova also advanced with ease, beating American Bernarda Pera with the loss of just two games. Vondrousova took just 64 minutes to dispatch Pera 6-0, 6-2.
But Elena Rybakina’s title defence ended without a ball struck as she withdrew before her scheduled opener with a gastrointestinal issue.
Sinner said both he and Kokkinakis had to deal with the variable desert wind in their early match.
“We both started off a little bit tight, it was a little bit breezy,” Sinner said. “But when I broke him for the first time I felt immediately much better.”
Well prepared
After advancing in 80 minutes, with 21 winners and just seven unforced errors, the Italian was pleased but far from overconfident.
“I’m not unbeatable, just well-prepared,” he said. “I worked really hard to be in this position…you dream of winning a Grand Slam.”
“You travel here, the conditions are different. You have to find a way somehow.”
Sinner ran off a dozen points in a row to earn a lead of a set and 3-0 and continued to apply the screws to his 99th-ranked opponent.
The Italian won the final 10 games to advance and will face either Jan-Lennard Struff or Borna Coric in the next round.
Alex de Minaur, the 10th seed coming off a triumph in Acapulco at the weekend, regained some Aussie pride as he crushed Japan’s Taro Daniel 6-1, 6-2.
German sixth seed Alexander Zverev opened his week with a 6-4, 6-4 victory over Australian Christopher O’Connell.
Zverev’s compatriot Angelique Kerber lifted the tempo of her maternity return as she upset fellow Grand Slam winner Jelena Ostapenko 5-7, 6-3, 6-3.
The 34-year-old German, who became a mum last summer and returned to the courts in January, won two consecutive matches for the first time since Wimbledon two years ago.
No 11 Greek Stefanos Tsitsipas beat Lucas Pouille 6-3, 6-2.