The American great, who lost the top ranking to Angelique Kerber last year, blitzed the unseeded 19-year-old 6-4, 6-3 on Rod Laver Arena in scorching temperatures as she hunts down a seventh Melbourne Park crown.
It sets her up for a clash with Lucie Safarova from the Czech Republic, who saved nine match points before beating Belgian Yanina Wickmayer in their first round encounter.
“She is a great player, recently rated in the top 10. It really was one of the toughest first round matches I have ever played,” Williams said of Bencic.
“I knew I had to be strong.”
“Right now I have nothing to lose,” added Williams, whose new fiance, Reddit co-founder Alexis Ohanian, was watching from the stands.
“Every match I play is for fun. It's self-motivating. I'm just happy to be playing.”
Asked how she rated her form, she said: “I think it was pretty good. She's a really good player, so I think I was able to start out well.
“I made a few errors on some key points, but for the most part, I still was going for everything and I was able to close it out.”
Williams, who lost last year's final to Kerber, came into the opening Grand Slam of the year with question marks over her form.
She has barely played since the US Open last September due to injury, and her build-up was set back when she was bundled out of this month's Auckland Classic in the second round.
But any doubts were quickly put to rest as she eased her way into the tournament, showing little emotion as she went about her business.
Both players held serve at the start as they probed for weaknesses, with Williams saving two break points in the third game before recovering to keep it at level pegging.
Bencic, a rising star whose 2016 was marred by injury, was making her work hard but it was the American who got the first break when the Swiss star looped a forehand long.
The advantage was short-lived, with Bencic bouncing straight back as Williams' serve let her down.
Bencic, 19, is a former world number seven and has form against Williams, stunning her in the 2015 Toronto semifinals in what remains the biggest win of her career.
But the composed Williams slowly got on top in Melbourne, breaking again in the 10th game as Bencic sent down a string of forehand errors.
The Swiss teen was getting frustrated, throwing her racquet to the ground as Williams broke again early in the second set.
The 35-year-old, in a black and white outfit, was in her groove and despite being broken in the seventh game and sending down a double fault on match point, was in control and eased to the finish line in 79 minutes.
Seeded two, Williams is attempting to break Steffi Graf's Open-era record of 22 Grand Slam singles titles, but has her work cut out if she is to go one better than the German great.
She could encounter either in-form Briton Johanna Konta, who won the lead-up Sydney International, or sixth seed Dominika Cibulkova in the quarterfinals.
Melbourne Park has been a happy hunting ground. She claimed her first Australian Open title way back in 2003, beating elder sister Venus in the final.