Simona Halep and Naomi Osaka also progressed as they saw off Sofia Kenin and Tamara Zidansek, respectively, while Venus Williams needed three sets to get past Alize Cornet.
Stan Wawrinka went out at the hands of 16th seed Milos Raonic in four hard-fought sets, while seventh seed Dominic Thiem retired two sets and a break down against Alexei Popyrin.
Kei Nishikori avoided an upset against Ivo Karlovic, but he needed five sets to do so.
Later in the day, No. 4 Alexander Zverev was also in action against Jeremy Chardy, while Novak Djokovic was last on court at the Rod Laver Arena as he faced off against Jo-Wilfried Tsonga.
U.S. Replay Info
TV: ESPN2 (12 p.m. ET), Tennis Channel (7 a.m. ET and 5 p.m. ET)
UK Replay Info
TV: Eurosport 1 (1:30 p.m., 4 p.m. and 6 p.m. GMT)
Live Stream: Eurosport Player
Selected Men's Singles Results
Alexei Popyrin bt. (7) Dominic Thiem, 7-5, 6-4, 2-0, ret.
(8) Kei Nishikori bt. Ivo Karlovic, 6-3, 7-6 (6), 5-7, 5-7, 7-6 (7)
(11) Borna Coric bt. Marton Fucsovics, 6-4, 6-3, 6-4
(16) Milos Raonic bt. Stan Wawrinka 6-7 (4), 7-6 (8), 7-6 (11), 7-6 (5)
Selected Women's Singles Results
(1) Simona Halep bt. Sofia Kenin, 6-3, 6-7 (5), 6-4
(4) Naomi Osaka bt. Tamara Ridansek, 6-2, 6-4
(6) Elina Svitolina bt. Viktoria Kuzmova, 6-4, 6-1
(7) Karolina Pliskova bt. Madison Brengle, 4-6, 6-1, 6-0
(16) Serena Williams bt. Eugenie Bouchard, 6-2, 6-2
Venus Williams bt. Alize Cornet, 6-3, 4-6, 6-0
Visit the Australian Open website to see the results in full.
Serena Williams extended her head-to-head record against Eugenie Bouchard to 3-0 on Thursday as they met for the first time since 2014.
The American broke the Canadian four times in the opening set, though she was broken twice herself.
In the second set, Bouchard rectified her failure to hold serve with an improved showing early on, per tennis writer Gaspar Ribeiro Lanca:
However, it soon went the same way as the first set, with Williams finishing confidently to see out the contest in little more than an hour.
Halep eased through her first set against Kenin in 34 minutes, and the world No. 1 was playing some fine tennis along the way:
The second set did not go to plan, however. After rushing to a 3-0 lead courtesy of an early break, Halep was quickly pegged back to 3-3 and subsequently lost in the tiebreaker against a resurgent Kenin.
The American was similarly impressive in the third set, but despite going a break up in the decider, she was unable to see out the win.
Meanwhile, Raonic and Wawrinka had to be separated by tiebreakers in every set they played in their four-hour epic.
After being edged out in the first, the Canadian came out on top in the three that followed against the 2014 champion.
The Press Association's Eleanor Crooks has been impressed with Raonic amid a difficult start in Melbourne:
Nishikori's match with Karlovic was similarly tight, as they shared just three breaks of serve between them in five sets. Nishikori's only break came in the first set, but it was little wonder he struggled to get near Karlovic's serve, as the Croatian produced an astonishing 59 aces over the course of the match.
After being pegged back from two sets up, the No. 8 seed eventually came out on top via a fifth-set tiebreaker.
Nishikori will meet Joao Sousa in the next round, with both players having gone to five sets in each of their first two matches.