The Dane regained her composure and went on to drop just one more game to book a quarter-final spot after an hour and 30 minutes of play on centre court.
Earlier in the day, Halep shrugged off a slow start to beat Latvian Anastasija Sevastova 6-4 6-3, keeping her hopes of regaining the number one ranking alive this week.
The 26-year-old Romanian rallied back from an early break and remained aggressive throughout, landing 29 winners to 21 unforced errors.
She converted five of eight break point opportunities to reach the last-eight in Doha for the first time since 2014.
Should Halep finish the tournament with one win more than Wozniacki, she will reclaim the top spot she lost after the Australian Open on Monday's ranking.
Halep will next face American CiCi Bellis, who claimed the biggest win of her career after overcoming world number five Karolina Pliskova 7-6(4) 6-3.
Bellis looked fairly comfortable against her Czech opponent's powerful serve, breaking her five times on her way to victory in an hour and 37 minutes.
"This was huge for me," 18-year-old Bellis, ranked 48 in the world, said.
"I think I played a really good match and just tried to track down as many balls as I could. Obviously, I've watched her play for many years and she's one of my idols for sure. I'm just really happy to was able to get through it."