A first set tiebreak was needed to settle the deadlock and it was the Australian open victor Wozniacki that eventually prevailed winning 7-4 to take the first set.
The injury to her right foot had forced out of the game since the Australian Open, where she lost the final to Wozniacki.
Simona Halep, the only former champion left in the draw, defeated 6-0 6-4 Catherine Bellis.
"I withdraw because I can not play anymore and it's going to be unsafe if I force it", she told reporters.
A resurgent Petra Kvitova beat world No. 3 Elina Svitolina 6-4, 7-5 to set up a quarter-final clash with another top-10 player, Germany's Julia Goerges. "I didn't have much time to recover before this tournament, but today was too much, and I chose to stop". "I am really disappointed by what she said and I think she gives herself too much importance".
The MRI shows that I have fluid and also tendonitis at the fourth toe.
Although she would take the match in straight sets, Wozniacki took serious umbrage with what she felt was Niculescu's excessive gamesmanship.
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"I think it's definitely a milestone".
Halep shrugged off injury concerns coming into the match about an ankle injury which had kept her out of action since Melbourne.
"And she will change the grunt according to what she feels like."Asked if she thought her opponent was grunting deliberately, Wozniacki responded: "I think that she didn't do it in the second set, so". Since then, I went up more and more, and now I'm here, making another quarterfinals in Doha".
Garbine Muguruza, who beat Caroline Garcia in the last-eight, earns a bye into Sunday's Doha final due to Halep's withdrawal.
In a post-match press conference, Wozniacki said: "She's a player that tries to get into your head. She is a great player, a great champion, and hopefully she will be back soon".
1-6, 6-3 to progress to the semi-finals in a high-quality contest lasting nearly two-and-a-half hours. "It's the only way she can win" Wozniacki said before going on to mock Niculescu's grunts.