Her sister, Venus Williams, suffered another first-round exit to 15-year-old Coco Gauff, however.
Roger Federer made it past Steve Johnson comfortably in three sets, while reigning women's champion Naomi Osaka and Petra Kvitova also progressed without incident.
Women's No. 1 seed and local favourite Ashleigh Barty had to come from behind to beat Lesia Tsurenko.
Defending men's champion Novak Djokovic was also in action in Melbourne and needed four sets to get past Jan-Lennard Struff.
Selected Men's Singles Matches
(3) Roger Federer bt. Steve Johnson, 6-3, 6-2, 6-2
(8) Matteo Berrettini bt. Andrew Harris, 6-3, 6-1, 6-3
Marton Fucsovics bt. (13) Denis Shapovalov, 6-3, 6-7 (7), 6-1, 7-6 (3)
(6) Stefanos Tsitsipas bt. Salvatore Caruso, 6-0, 6-2, 6-3
(2) Novak Djokovic bt. Jan-Lennard Struff, 7-6 (5), 6-2, 2-6, 6-1
Selected Women's Singles Matches
(8) Serena Williams bt. Anastasia Potapova, 6-0, 6-3
(3) Naomi Osaka bt. Marie Bouzkova, 6-2, 6-4
Coco Gauff bt. Venus Williams, 7-6 (5), 6-3
(7) Petra Kvitova bt. Katerina Siniakova, 6-1, 6-0
(1) Ashleigh Barty bt. Lesia Tsurenko, 5-7, 6-1, 6-1
Shuai Zhang bt. (24) Sloane Stephens, 2-6, 7-5, 6-2
Full results can be found at the Australian Open's official website.
Serena Williams needed just 58 minutes to sweep Potapova aside, picking up a bagel in the opening set.
The seven-time Australian Open singles winner wasted no time in demolishing the 18-year-old:
The Russian gave a better account of herself in the second set and was briefly a break up against the 38-year-old, but there was little she could do against a confident performance from Williams.
Meanwhile, in the battle between the youngest and the oldest entrants in the women's draw, it was the former who came out on top.
Just as she did at Wimbledon last year, Gauff picked up a straight-set opening-round win over 39-year-old Venus Williams.
The Floridian eventually edged out the veteran in a first-set tiebreaker after Williams had saved three set points at 5-4. In the second, she raced to a 3-0 lead before seeing out the set, and tennis writer Tumaini Carayol was impressed:
Federer played his first competitive match since November, but the 38-year-old showed little sign of rust as he dispatched Johnson in just 82 minutes without giving up a break of serve.
The American was limited to just one break-point opportunity in the entire contest.
Christopher Clarey of the New York Times gave his take on the Swiss maestro after the first set:
Osaka impressed as she kicked off her title defence against Marie Bouzkova.
After a comfortable first set, Osaka found herself 2-4 in the second after falling a break behind, but she finished the match with four consecutive games to avoid a third set.
A shaky start from Barty saw her broken three times by Tsurenko in their opening set, but she put in a much more solid performance as she dropped just two of the final 14 games:
Stefanos Tsitsipas reached the semi-finals in Melbourne last year, but he also suffered first-round exits at both Wimbledon and the U.S. Open.
There was no danger of that here, though. The 21-year-old did not give up a single break-point chance to Salvatore Caruso as he set up a second-round clash with Philipp Kohlschreiber.
Djokovic recorded his 900th career victory against Struff, but he didn't have it all his own way against the German.
After requiring a tiebreaker to take the first set, he looked to be on course to win in three when he took the second 6-2. Struff fought back and took the third, however, with the aid of back-to-back double-faults at the end of the set from the No. 2 seed.
That proved to be the wake-up call Djokovic needed, and he dropped just one game on his way to taking the fourth.