This match is unlikely to feature in a compilation of the Dane’s greatest hits, but her willingness to batten down the hatches and scrap for every point helped her overcome early adversity.
Sasnovich, immensely talented but erratic, started with an avalanche of winners but then struggled to maintain such a high level. She stormed into a 4-1 lead before a series of double-faults upset her rhythm.
Wozniacki capitalised on her rival’s serving crisis and reeled off five games in a row snatch the first set from an unlikely position.
The No.2 seed was in control, but the Belarusian responded impressively. She nabbed a break in the first game of the second set and her confidence returned as a result.
It was hard not to assume that Sasnovich would once again squander her advantage, but she increased her lead and eventually took the set by six games to two.
There was growing concern within the Dane’s camp when their charge nudged a backhand wide to fall a break behind in the decider, however it was just a minor blip.
The Australian Open champion used her renowned retrieval skills to extract errors from her opponent, and she narrowly avoided becoming the latest seed to be dumped out the competition.
Sasnovich, who started the year impressively by coming through qualifying and reaching the final of the Brisbane International, was let down by her serve.
The 23-year-old committed an eye-watering 14 double-faults, and against the world No.2, that was never going to be good enough.
“It was definitely a hard day at the office,” admitted the Dane post-match. “I’m not a morning person so it felt pretty early out there for me but I tried my best.
“Sasnovich started really well and I couldn’t really find my rhythm. It was a battle, and I was just trying to get into the match and to play better in the first few balls of the points.
“I stayed mentally tough out there, and that’s why I won today.”
Wozniacki will play either Sloane Stephens or Daria Kasatkina in the fourth round on Wednesday.