"She fought very hard today and so did I," said Wozniacki. "I just got a little lucky in the end and it could have gone either way.
"It's enjoyable when you win in the end, when you are playing well, and your opponent is playing well. You push each other to play at a high level - those are the fun matches to play."
The diminutive Davis (1.57m) is always underrated, but proved her class here in 2017, when she came through a field containing the Williams sisters, Wozniacki and Naomi Osaka to claim the title.
The 26-year-old was at her pugnacious best on Thursday night, coming back into the match after a forgettable first set, where Wozniacki seemingly broke her serve at will, though the final game stretched on for 10 minutes before the Dane finally sealed the set.
The world No 54 reset from there, and used intelligent court craft and great angles to pin Wozniacki well behind the baseline.
Davis forced two set points, at 5-3, but couldn't take them, as Wozniacki fought back. But, typical of this encounter, Wozniacki then dropped serve, to give Davis the set.
"Obviously I didn't want to play a third set," said Wozniacki. "But it was what it was, and she played some really great points there at the end of the second set and that was that."
That set up a fantastic, frenetic final set, where the tennis hit new heights.
The momentum swung throughout, with five breaks of serve, and the ninth game produced some spectacular rallies, with Davis left on her knees a couple of times, as Wozniacki turned her inside out.
The Dane had her own wobbles, and was relieved to serve out the match, with Davis forced into some uncharacteristic cheap errors.
Wozniacki will play two-time defending champion Julia Goerges in the last eight on Friday, a repeat of the 2018 final, before a doubles semifinal alongside Serena Williams.
"I'm ready for it," said Wozniacki, when asked about the workload. "When I train, I train very hard, with long hours so I am ready to play both."
