Wozniacki followed up her 6-0, 6-2 victory over Christina McHale from Wednesday with the 6-1, 6-0 win over Dulgheru - after Dulgheru held in the fourth game of the match, Wozniacki won nine in a row.
"I played really well tonight. I started off strongly and played aggressively, came to the net a few times, served well - yeah, it was a good performance. I was really excited about it," Wozniacki said.
"Honestly I want to keep going the way I've been doing. I've been working really hard in the off-season and I'm happy that it's showing, and that I can implement some of those things into my game.
"It's always a great atmosphere here at the ASB Classic - that's why I love coming back, and that's why I wanted to start my year here. It's a great tournament and I love playing in front of everybody."
Things could get a lot tougher for the No.3-seeded Wozniacki, though, as up next is the only other seed left in the draw, No.5 seed Sloane Stephens, who cooled off British qualifier Naomi Broady, 7-6(6), 6-3, saving two set points in the first set - one of them down 6-5, another down 6-5 in the tie-break.
Wozniacki has beaten Stephens in all five of their previous meetings, but Stephens has played some of her very best tennis in the Australian season - she was an Australian Open semifinalist in 2013.
"Sloane's a great player and it's going to be a tough one tomorrow," Wozniacki said. "I've played really well against her in the past, but it's a new year and a new tournament. It's never been an easy one against her. I'm just excited to get another challenge out there and I hope I can keep my level."
The other semifinal will pit Julia Goerges, a former Top 20 player, against Austrian qualifier Tamira Paszek, a two-time Wimbledon quarterfinalist. Goerges rallied to beat Nao Hibino, 6-7(3), 6-2, 6-4, while Paszek beat Belgian qualifier Kirsten Flipkens in another three-setter, 6-4, 6-7(3), 6-3.