Halep, a beaten finalist at Melbourne Park two years ago, moved on with a 6-4 6-4 victory that sets up a meeting with Estonia’s 28th-seed Anett Kontaveit in the last eight.
Simona Halep had to be at her counter-punching best to fight off another determined second-set comeback bid from Elise Mertens on Monday as the Romanian world number three advanced to the quarter-finals of the Australian Open.
Halep, a beaten finalist at Melbourne Park two years ago, moved on with a 6-4 6-4 victory that sets up a meeting with Estonia's 28th-seed Anett Kontaveit in the last eight.
Halep had lost to Mertens in the Doha final last year when up a set and cruising in the second and the Romanian conceded nerves crept into her game as the momentum shifted on Monday.
"Against her in Doha in the final, I was leading a set and 4-2 and lost the match so I knew I had to stay focused until the end," the two-time Grand Slam champion said.
"To be honest I got a bit nervous at 4-3 (in the second).
"I had in my head she came back in that match, and I have just to pay attention on every ball, not giving up at all, because she can come back strong."
Mertens blasted bags of winners but also made 38 unforced errors as Halep chased down every ball and made the Belgian work for every point.
The fourth seed's confidence will have been boosted by the way she was able to raise her game on Monday as she battled the Belgian in lengthy rallies of high-quality shot-making.
Halep managed to crack Mertens at crucial moments, breaking for the second time to go 5-4 up in the first set and then serving it out.
She jumped out to a double break 3-0 lead in the second but Mertens came storming back and leveled at 4-4 as a frustrated Halep remonstrated with her box and whacked her racquet into the ground without breaking it.
That outburst seemed to help Halep as she put Mertens under intense pressure in the 11-minute ninth game, which she took on her fifth break point opportunity then sealed the win on her next service game.
"Mentally I think I did a great job today at four-all with those breakpoints, game points," she said.
"In the end, I got the game and then I served very well the last game.
I feel like I played a better match than all the matches since I'm here."
Muguruza powers past Bertens into last eight
Garbine Muguruza powered into the Australian Open quarter-finals with a 6-3 6-3 demolition of ninth-seed Kiki Bertens in just 68 minutes on Monday.
Muguruza, a former French Open and Wimbledon champion, was unseeded at Melbourne Park and has proved a dangerous floater in the draw, having also thrashed fifth seed Elina Svitolina 6-1 6-2 in the previous round.
The 26-year-old Spaniard, who was rusty before the tournament after withdrawing from Hobart with a virus and then lost the first set of her first round clash with Shelby Rogers 6-0, was almost unstoppable on Monday.
She broke Bertens five times throughout the match, including in the final game, and clinched a quarter-final with either Angelique Kerber or Anastasia Pavlyuchenkova when she blasted a forehand winner down the line.