The 37-year-old American, whose 23rd major title came in Melbourne when she was pregnant two years ago, won 6-0 6-2 in 49 minutes on Rod Laver Arena.
Williams holds the most Open era singles titles, but is looking to equal Margaret Court's all-time record of 24.
Sister Venus dug deep to beat Mihaela Buzarnescu 6-7 (3-7) 7-6 (7-3) 6-2.
The Romanian 26th seed served for the match at 5-3 in the second set but Venus broke to love.
The 38-year-old American, ranked 36th, went on to take the set before dominating the third.
The seven-time Grand Slam champion said: "It was pretty hairy there. I hope that this tough match will prepare me for the rest of the tournament."
Williams, who has reached the final at Melbourne Park twice, most recently in 2017 when she lost to Serena, will meet Alize Cornet of France next.
Serena still has health concerns
Serena, the 16th seed, took the first set in 18 minutes against Germany's Maria and fired 22 winners during her opening match.
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