After cruising through the first set in just 28 minutes and breaking to go up 2-1 in the second set, Halep got broken back for 2-all - then broke and got broken back for 3-all, then broke and got broken back for 4-all. So when she broke at love in the next game the deal didn't seem sealed by any means.
But the No.1-seeded Halep finally broke the break-fest, serving out a 6-2, 6-4 victory.
Halep is now through to the quarterfinals or better at a WTA tournament for the seventh time this year, winning one title (Doha), reaching two more finals (Madrid and the French Open), two semifinals (Indian Wells and Wimbledon) and now two quarterfinals (the Australian Open and Bucharest).
"It was a very difficult match today," Halep said. "It was very warm and there was a lot of humidity too, but I'm happy I could win in two sets again and keep enjoying playing at this tournament."
Halep was particularly happy with the reception she got from her home fans at the match.
"It didn't matter that the rain came, they stayed for me, and I appreciate that a lot!"
Next up for Halep is Lara Arruabarrena, who has had to go to third set tie-breaks in both of her first two rounds, against No.5 seed Annika Beck in the first round and Cagla Buyukakcay in the second round (and in that match against the Turkish No.1 she had to had to come from double match point down).