Cibulkova and Sharapova were among the women's third round winners at the Australian Open on Saturday along with Garbine Muguruza, Victoria Azarenka, Jelena Jankovic, Agnieszka Radwanska, Sloane Stephens and Simona Halep.
The biggest casualty of the day was former long-time world No.1 Caroline Wozniacki who was upset in three sets by the unseeded Spaniard Muguruza.
First up on Rod Laver Arena on Saturday in women's third round action was the first of the former world No. 1s to play on the day as Russian No. 3 seed Maria Sharapova took on French 26th-seed Alize Cornet.
The Russian had to get through a marathon second round clash with Italian Karin Knapp in the middle of the Melbourne heat, but she was showing no signs of that to start her clash with Cornet racing through the first set dropping just the one game.
However, Cornet has had a terrific summer in Australia having already teamed with Jo-Wilfried Tsonga to win the Hopman Cup in Perth, and she put up a strong fight in the second set.
In the end, though, the experience and big stroke-making ability of the 2008 Australian Open winner was too much for Cornet as Sharapova won the second set eight points to six in the tie-break to take out the match 6-1, 7-6 (6).
Again though, it was far from a commanding performance from Sharapova as she hit eight double faults and 35 unforced errors, but she did well to convert six breaks of serve and to win 12-of-13 points at the net.
Next up in women's action on Rod Laver Arena saw two-time year-end No. 1 Caroline Wozniacki taking on talented unseeded Spaniard Garbine Muguruza.
Muguruza might only be ranked 38 in the world and never having done better than making a Grand Slam second round before, but she has all the tools to match it with the big guns of women's tennis and showed exactly that against the Danish 10th-seed on Saturday.
Wozniacki did manage to win the first set, but then the Spaniard turned her game up a notch and won the next two sets to win the match 4-6, 7-5, 6-3 and win her way into the Australian Open fourth round where she will take on world No. 5 Radwanska.
The night session on Rod Laver Arena then began with defending Australian Open champion Victoria Azarenka putting on a dominant display against Austria's Yvonne Meusburger, winning 6-1, 6-0 to cruise into the fourth round.
Women's third round action began on Hisense Arena with another former world No. 1 in action with Serbia's Jelena Jankovic playing her third Japanese opponent in a row, Kurumi Nara.
And it was a tight contest through the two sets, but the eighth-seeded Jankovic did enough to advance to the fourth round with her 6-4, 7-5 victory.
Next up on Hisense Arena was a fantastic women's third round battle between fifth-seeded Pole Agnieszka Radwanska and 29th-seeded Russian Anastasia Pavlyuchenkova.
Pavlyuchenkova managed to take a one-set lead as well to be within touching distance of an upset, but the world No. 5 steadied to win the next two sets while dropping only four games in total, and she won the match 5-7, 6-2, 6-2.
Seven double faults, 49 unforced errors and winning just 46 per cent of her second serves proved costly for Pavlyuchenkova as an efficient Radwanska hit five aces, 25 winners, just 19 unforced errors and converted 6-of-9 break points.
The thrashing of the day in women's action took place on Margaret Court Arena with 20th-seeded Slovak Dominika Cibulkova crushing a tired Spanish 16th-seed Carla Suarez Navarro, 6-1, 6-0.
Suarez Navarro had to fight through three hours and 10 minutes to beat Kazakhstan's Galina Voskoboeva in the second round to advance to the third round, and it clearly took its toll as Cibulkova made her pay backing up her equally crushing second round win over Swiss Stefanie Voegele.
Suarez Navarro managed to win only 26 points in total for the entire match while hitting only two winners and winning just 27 per cent of her second serve points.
Cibulkova will now look to keep her remarkable form going against Sharapova in the Round of 16.
Next up on Margaret Court Arena was American Sloane Stephens taking on the Ukraine's Elina Svitolina, and the 13th-seeded Stephens proved too good with the 20-year-old advancing to the Round of 16 with a 7-5, 6-4 victory over her world No. 47 opponent.
Stephens will now take on Azarenka in what is sure to be a fascinating Round of 16 match-up.
Meanwhile out on Court 3, Romania's 11th-seed Simona Halep has quietly progressed into the fourth round with a crushing 6-1, 6-4 victory over Kazakhstan's Zarina Diyas.
Halep's next challenge in the fourth round is a clash with Jankovic.