In the men's draw, veteran Federer topped Steve Johnson from the United States 6-3, 6-2, 6-2, and Greece's Tsitsipas dispatched Salvatore Caruso 6-0, 6-2, 6-3, despite a late fightback from the Italian.
Seven-time Australian Open winner Djokovic progressed with a hard-fought 7-6 (5), 6-2, 2-6, 6-1 victory against Germany's Jan-Lennard Struff at the Rod Laver Arena.
"It's great to be back in this arena that has a very special place in my heart," Djokovic said in a post-match interview.
"This has been by far my most successful court in my career and I love coming back to Australia, the land of tennis."
Local hopeful and women's World No. 1 Barty had the home crowd on edge after losing the first set against Ukraine's Lesia Tsurenko, but she dominated the remainder of the contest with a final score of 5-7, 6-1, 6-1.
One of the day's surprises was a deja vu win for China's Zhang Shuai, who staged a dramatic comeback to topple U.S. competitor Sloane Stephens 2-6, 7-5, 6-2.
The scoreline was eerily similar to that at the 2018 Australian Open, when the two women met in the first round, on the same court, with Zhang also triumphing after dropping the first set, 2-6, 7-6, 6-2.
Another shock was the departure of 13th ranked Canadian Denis Shapovalov, who went down to Hungary's Martin Fucsovics 6-3, 6-7, 6-1, 7-6.
The hot-headed Canadian youngster exchanged words with the umpire after receiving a code violation for slamming his racquet on the ground.
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