With temperatures down a few degrees from the torrid 40 Celsius (104 Fahrenheit) earlier in the day, Halep helped exact some revenge from the last -- and only -- time the pair met in a Grand Slam tournament.
At Wimbledon in 2014, the Canadian beat Halep in the semifinals before advancing to the final, where she lost to Petra Kvitova.
Her strong run early that year -- making the semifinals at the Australian and French Opens before Wimbledon -- helped propel Bouchard to No. 5 in the rankings. She has since had a major slide and is now ranked 112th.
With a forecast high of 39 Celsius (102 Fahrenheit), Maria Sharapova appeared to be in a hurry to get off the Rod Laver Arena court in the earlier match, winning the first set in 23 minutes.
The five-time major winner advanced to the third round with a 6-1, 7-6 (4) win over No. 14-seeded Anastasija Sevastova.
"It's a warm day. I did my job in two sets against someone that's been troubling in the past for me," said Sharapova, who missed last year's tournament while serving a 15-month doping ban. "So, third round of the Australian Open, I don't know, I think I deserve to smile out there after that victory."
Sharapova is playing at Melbourne Park for the first time since her suspension for testing positive for meldonium at the 2016 Australian Open. She lost to Sevastova in the fourth round at the US Open last September in her return to Grand Slam tennis.
"I look forward to these matches. I want to be playing against opponents that have former Grand Slam champions," Sharapova said of a potential match against former No. 1-ranked Kerber. "She's had success playing out here in these conditions on these courts. I want to see where I am on that level."
Wimbledon champion Garbine Muguruza struggled with the heat and against Hsieh Su-wei's game, losing 7-6 (1), 6-4 on Day 4 as the upsets intensified.
Muguruza had five double-faults, including one to give Hsieh a match point, and made 43 unforced errors. She needed a medical timeout in the first set and accidentally hit a ball into a line judge in frustration.
"She's definitely a very tricky opponent -- today she played well,'' said Muguruza, acknowledging that the heat was bothersome but it wasn't the hottest conditions she'd experienced in Australia. "I could have done things better, but at the end, she deserves to win.''
The 32-year-old Hsieh is a former top-ranked doubles player who had only one previous win over a top-10 player and whose career-high singles ranking peaked at 23 in 2013.
Considered one of the contenders for the title after Serena Williams opted against defending her Australian Open title, Muguruza had a troubled preparation. She retired with cramps in the second round at the Brisbane International and withdrew before her quarterfinal at Sydney because of a right thigh injury.
It was Kerber's 11th win in a row to start the season. Kerber won four singles matches at the Hopman Cup and five more while winning last week's Sydney International. She beat fellow German Anna-Lena Friedsam in the first round here.
The crowd sang "Happy Birthday'' and gave three hoorays to celebrate Kerber's 30th birthday.
"Happy to be playing tennis again like 2016,'' said Kerber, who planned an ice bath before a relaxed dinner out in Melbourne to mark the occasion.
Ninth-seeded Johanna Konta was more exposed to the heat on an outside court and lost to U.S. lucky loser Bernarda Pera 6-4, 7-5.
No. 123-ranked Pera is making her Grand Slam debut and, after losing in the last round of qualifying, didn't even know she had a spot in the main draw until Monday, when Russia's Margarita Gasparyan withdrew with an injury.
Konta saved three match points in the ninth game of the second set, then broke Pera to level at 5-all.
But Pera clinched it on her fifth match point when Konta, a semifinalist here in 2016, shanked an overhead at the net.
"It feels amazing," Pera said. "I was ready to leave on Monday, and then they told me I'm in, so I was obviously excited. I was checking the tickets to fly back. I'm happy I didn't buy one."
Pera will next play No. 20 Barbora Strycova, who beat Lara Arruabarrena 6-3, 6-4.
The 17th-seeded Keys was dominant serving in the first set. She served five aces in six attempts to open the match -- four in the first game and another on the second point of her next service game. She won every point on her serve in the first set, holding at love in three games.
The Associated Press contributed to this report.