It was a battle of former Wimbledon finalists and semifinalists in Melbourne as the No. 4 seed prevailed over the tentative 21-year-old from Canada, whose ranking -- once among the top five -- has fallen to No. 37.
Bouchard is now a telling (and dismal) 1-10 against players ranked in the top five.
"I'm very happy with my game," Radwanska said afterward. "It was not an easy match. She is playing much better. I was glad I could win the match in two sets."
Bouchard was up 4-2 and actually held a set point in the first frame, but lost three consecutive points, spraying a makeable forehand long, dumping a big serve into the net and watching a terrific forehand winner fall as Radwanska converted her fourth set point.
That was essentially that, because Radwanska was 24-1 in Melbourne after winning the first set.
Make that 25-1.
Even Radwanska's vision was spot on; she won the match by challenging a baseline call and a replay supported her belief.
Bouchard's calling card in the past has been taking the ball early and mastering acute angles. Against Radwanska, however, she committed 37 unforced errors, against 25 winners. Radwanska was more efficient, hitting nine winners and 12 unforced errors. Radwanska also converted all four of her break-point opportunities, while Bouchard was a sloppy 1-for-7.
Pliskova, who is ranked No. 114 in the world and is the twin sister of No. 9 seed Karolina Pliskova, broke Sabine Lisicki's previous mark of 27 aces. That wasn't enough for the Czech player to win, though, as she made 53 unforced errors against Puig.
"I don't care right now,'' Pliskova said of the record after the loss.
The two-hour, 20-minute match was so close that each player won 115 points. Pliskova had a chance to win but could not convert three possible match points in the second set. She had 12 aces in the third set but lost again.
"I had many match points so I'm really sad about that," Pliskova said.
Meanwhile, Petra Kvitova, who missed two tournaments this month due to a stomach virus, clearly was not at full strength when the sixth-ranked player lost in straight sets to Australian Daria Gavrilova, 6-4, 6-4.
"I'm over the illness. It might be a combination of the physical and mental things, like nerves,'' Kvitova said. "It just felt a little weird. I'm not ill -- maybe in the head -- but I couldn't do what I wanted to prepare. It was pretty humid here today and I was breathing pretty heavily tonight.
"I felt good in the first-round match but I don't think it was as physically as tough as today. I had to move well today, which I didn't. It wasn't just about the matches, but when I was ill, I could not do what I wanted physically.''
Radwanska is now 2-0 for her career against Bouchard, following a 2014 victory in Madrid.
While most eyes have been on No. 1-ranked Serena Williams since her stunning loss at the US Open, which ended her quest for a calendar-year Grand Slam, Radwanska has been carving out one of the best records in women's tennis. The 26-year-old Pole has won more titles (four) and more matches (24) than anyone. She's an impressive 24-4 since losing in the third round at New York to Madison Keys.
Radwanska is now 7-0 in 2016. Two years ago, she lost in the Australian Open semifinals to Dominika Cibulkova. Ten of Radwanska's 18 career WTA titles have come in the Asia-Pacific. If the seeding holds, she could face Serena Williams in the semifinals. She has never won a Grand Slam tournament.
Neither, despite a promising start to her career, has Bouchard, who acknowledged she had a "weight on her shoulders" from an exceptional 2014 season before struggling in 2015.
That was punctuated by a concussion sustained during a fall in a US Open locker room, which caused her to pull out before her fourth-round match. She exited 2015 ranked No. 46, down from No. 7 the previous year.
Working on her fourth coach in two years, Thomas Hogstedt, Bouchard was unseeded at a Grand Slam for the first time since the 2013 US Open.
ESPN Staff Writer Jim Caple contributed to this report.