She had to save two match points in the second round and shrug off a mental lapse while serving for the match in the semifinals. She then had to summon the guts, the energy and the accuracy on the run to prevail against Halep, weary but still dangerous, in Saturday’s 2-hour-49-minute final played on a sweltering Australian summer evening.

“I think I had everything else on my résumé,” Wozniacki said later, the trophy glittering by her side. “No. 1, year-end championships, big tournaments, 27 titles. I basically have beaten any player that has been playing that is on tour right now. This was the only thing missing, and it means something extra even that it took a little longer, but I still made it here.”

Halep, a Romanian, will lose her No. 1 ranking to Wozniacki on Monday, and knows all too well about delayed gratification. She is now 0-3 in major single finals and has lost all of them in three sets.

“Maybe the fourth time will be with luck,” she said in remarks to the crowd at Laver Arena, before leaving the court.

“It’s fine,” she said later. “I cried, but now I’m smiling. Is just a tennis match in the end. But yeah, I’m really sad I couldn’t win it. It was close again, but the gas was over in the end. She was better. She was fresher. She had actually more energy in the end.”