The second-seeded Wozniacki won the first seven games of the match but trailed 4-2 in the second set before staging a comeback. Suarez Navarro had to save one match point in the 10th game before Wozniacki was outclassed in the tiebreaker.
Wozniacki had an early break in the deciding set to take a 4-2 lead, then broke again in the seventh game before serving out the match in 2 hours, 11 minutes.
Wozniacki, who can return to the No. 1 ranking with her first Grand Slam singles title, plays Elise Mertens in the semifinals.
Mertens beat fourth-seeded Elina Svitolina 6-4, 6-0 earlier Tuesday to extend her winning streak to 10 matches. Mertens became the first Belgian since Kim Clijsters in 2012 to reach the semifinals here.
"If you believe in yourself, then anything can happen," Mertens said. "But of course semis is, 'Wow.'"
Mertens, who trains at Clijsters' academy, added: "Kim, thanks for watching, I knew you sent me a message before the match -- don't be too stressy."
"I'm trying to be in your footsteps this week."
Mertens, who was coming off a successful title defense at the Hobart International, dominated against Svitolina, who had also been on a nine-match winning roll after winning the Brisbane International.
Svitolina had won their only previous tour-level match, but had no answers on Rod Laver Arena and later said hip trouble had been bothering her all year.
"She played great from the beginning of the year," Svitolina said. "But, you know, when I give her opportunities to play and to play a good level, then of course she's going to play. She's going to go for shots.
"Now she's in semifinal. Now she's not just a player that's up-and-down. She's quite consistent, and we can see this."
Mertens, 22, was one of the biggest movers on the women's tour in 2017 as she improved her year-end ranking from 120 to 35 and won her first career title.
Information from The Associated Press was used in this report.