The Russian star prevailed 6-4, 4-6, 6-3 in two hours, 24 minutes of supreme tennis on Rod Laver Arena.
Meanwhile, Roger Federer, the men's defending champion, eased to a 6-2, 7-5, 6-2 victory over America's Taylor Fritz.
And No. 2 seed Rafael Nadal put on a clinic as he beat home favourite Alex de Minaur 6-1, 6-2, 6-4.
Selected Friday Results
(3) Roger Federer bt. Taylor Fritz: 6-2, 7-5, 6-2
(2) Rafael Nadal bt. (27) Alex de Minaur: 6-1, 6-2, 6-4
(6) Marin Cilic bt. (26) Fernando Verdasco: 4-6, 3-6, 6-1, 7-6 (8), 6-3
Tomas Berdych bt. (18) Diego Schwartzman: 5-7, 6-3, 7-5, 6-4
(20) Grigor Dimitrov bt. Thomas Fabbiano: 7-6 (5), 6-4, 6-4
(22) Roberto Bautista Agut bt. (10) Karen Khachanov: 6-4, 7-5, 6-4
(15) Ashleigh Barty bt. Maria Sakkari: 7-5, 6-1
(30) Maria Sharapova bt. (3) Caroline Wozniacki: 6-4, 4-6, 6-3
(2) Angelique Kerber bt. Kimberly Birrell: 6-1, 6-0
(5) Sloane Stephens bt. (31) Petra Martic: 7-6 (6), 7-6 (5)
(8) Petra Kvitova bt. Belinda Bencic: 6-1, 6-4
Full results can be found at the Australian Open's official website.
Sharapova was always likely to cause Wozniacki problems.
The 31-year-old is a five-time Grand Slam champion, including the 2008 Australian Open, and had dropped just three games in her opening two matches this year in Melbourne.
Wozniacki, 28, had also enjoyed relatively easy victories in her opening two matches at the 2018 Australian Open, and she raced into a 4-1 lead in the first set against Sharapova.
A double fault at break-point down in the seventh game of the set handed the break back to Sharapova, and it proved fatal as the Russian went on to win the opener by claiming five games on the bounce:
The Danish third seed was not quelled, though, and broke in the final game of the second set to level up the match.
It was a contest that deserved a decider given the quality of the two players, but Sharapova also deserved the win in the end.
She reapplied the pressure in the third set and showed a determination that has been in short supply since she returned from her doping ban in 2017.
The world No. 30 backed that up with plenty of quality, hitting 37 winners in the match to Wozniacki's 10, and displaying clinical finishing at the net.
Nadal was not so much clinical as brutal in his win over Australian De Minaur.
The Rod Laver Arena got behind the 19-year-old, who put in a spirited display, but Nadal was relentless in his pursuit of victory:
De Minaur simply could not live with Nadal's power as the Spaniard crushed winner after winner off his incomparable forehand.
When the teenager had the ball in hand, he had to work hard game after game simply to hold his serve, with Nadal claiming five breaks in the match.
Meanwhile, De Minaur rarely got close to breaking Nadal as he landed 75 per cent of first serves, winning 53 of 65 points behind it.
To his credit, De Minaur made Nadal work for two hours, 22 minutes before he sealed his spot in the fourth round, where he will face Tomas Berdych:
Federer, meanwhile, needed only 88 minutes to see off Fritz.
The Swiss third seed is going for a third consecutive title in Melbourne and set up a meeting with No. 14 seed Stefanos Tsitsipas by winning on Friday.
Against 21-year-old Fritz, Federer won 93 per cent of points behind his first serve, claimed 15 of 18 points at the net and hit 34 winners.
He and Nadal have looked ominously good in the first week and seem on a collision course to meet in the semi-finals.