The second-seeded former world No. 1 Sharapova blitzed helpless 31st-seeded Kazakhstani Zarina Diyas 6-1, 6-1 in 61 minutes at Laver Arena.
"I started really focused, I knew I had a tough, long match previously, so I wanted to start off strong and finish strong," said Sharapova.
"I think I did a good job of that."
Sharapova captured the Aussie Open in 2008 and was the runner-up here in 2007 and 2012. The five-time major champ will face Chinese Peng Shuai in the fourth round on Sunday.
Meanwhile, the No. 3 seed Halep fought past American Bethanie Mattek-Sands to reach the fourth round with a 6-4, 7-5 decision. Halep led 4-1 in the second set before Mattek-Sands mounted a mini comeback, only to fall short in the end.
Up next for the Romanian Halep will be Belgian Yanina Wickmayer.
The seventh-seeded Canadian star Bouchard had a tough first set but ended up cruising in the second to get past capable Frenchwoman Caroline Garcia 7-5, 6-0.
"I don't think it was the prettiest tennis out there today," admitted Bouchard, who has a big fan base in Australia.
Her fourth-round opponent will be Romania's Irina-Camelia Begu.
Tenth-seeded Russian left-hander Ekaterina Makarova defeated 22nd-seeded Czech and last week's Sydney runner-up Karolina Pliskova 6-4, 6-4, while Wickmayer pulled off an upset of 14th-seeded former French Open runner-up Sara Errani, of Italy, 4-6, 6-4, 6-3.
In some other third-round action, the 21st-seeded Peng battled her way past Kazakhstan's Yaroslava Shvedova 7-6 (9-7), 6-3, German Julia Goerges topped Czech Lucie Hradecka 7-6 (8-6), 7-5, and Begu dismissed German Carina Witthoeft 6-4, 6-4. Goerges should have her hands full with Makarova on Sunday.
The third round is scheduled to conclude on Saturday, including matches for top-seeded five-time Aussie champion Serena Williams, fourth-seeded Wimbledon titlist and last week's Sydney winner Petra Kvitova and 18th-seeded former Aussie finalist Venus Williams.
The 18-time Grand Slam champion and reigning U.S. Open queen Serena will take on 26th-seeded Elina Svitolina, while the left-handed Kvitova will tangle with rising American Madison Keys and the former No. 1 and seven- time Grand Slam champion Venus will encounter talented Italian Camila Giorgi.
Also on Day 6, sixth-seeded former Wimbledon runner-up Agnieszka Radwanska will meet 30th-seeded American Varvara Lepchenko; 11th-seeded 2014 Aussie runner-up Dominika Cibulkova will battle 19th-seeded Frenchwoman Alize Cornet 25th-seeded Czech Barbora Zahlavova Strycova will face former world No. 1 star Victoria Azarenka; and Coco Vandeweghe will lock horns with fellow American and last week's Hobart runner-up Madison Brengle. Cibulkova was last year's Aussie runner-up to since-retired Li Na.
The two-time Aussie Open champ and two-time U.S. Open runner-up Azarenka titled in Melbourne back-to-back in 2012 and 2013 before being slowed by a foot injury last year. She appears to be completely healthy now and ready to make a deep run at this fortnight.