Maria Sharapova has powered into the second week of the Australian Open with a 6-1 7-6 (8-6) win over Alize Cornet.

In milder temperatures than had greeted players previously this week, the Russian third seed started sharply, breaking Cornet twice before the Frenchwoman could settle into a rhythm.

With devastating groundstrokes, particularly her inside-out forehand and cross-court backhand, Sharapova was crushing Cornet as if she was first-round fodder rather than the 25th seed.

Cornet was gifted a break in the fifth game as Sharapova made a string of errors but the 2008 Open champion resumed normal service by immediately breaking back to love and serving out the set.

Putting up a stronger challenge in the second set, Cornet took advantage of Sharapova’s failing serve to break and lead 3-1 with a stunning drop volley.

Sharapova responded as she did in the first set, breaking to love to steady the ship.

The two traded breaks to land in a tiebreak, where Sharapova saved a set point before triumphing 8-6 and ending Cornet’s Australian Open in the third round for the fourth straight grand slam after one hour and 51 minutes.

Sharapova, who spent three-and-a-half hours on court in intense heat for her second-round match, was aware of the need to lift her game for the tournament’s second week.

“I definitely need to step it up. It always gets tougher from here,” she said.

“After the last match I’m just happy to get through this one and have another day to recover.”

The Russian said the “really welcome” change in weather might lead to a change in post-match routine.

“I might need to take a hot bath instead of a cold one,” she said.

Sharapova set up an intriguing fourth-round encounter with 20th seed Dominika Cibulkova, who was ruthless in her 6-1 6-0 demolition of injury-hampered Spanish 16th seed Carla Suarez Navarro.

The Slovakian hit 20 winners, has not dropped a set at the Open in three matches and has repeated her best performance at Melbourne Park with her fourth-round appearance.

Fifth seed Agnieska Radwanska is into the last 16, but had to do it the hard way with a three-set win.

Radwanska dropped the first set against Russian Anastasia Pavlyuchenkova, but responded to win 5-7 6-2 6-2.

Tenth seed Caroline Wozniacki, meanwhile, wasn’t as fortunate, going down 4-6 7-5 6-3 to Spain’s Garbine Muguruza.

Serb eighth seed Jelena Jankovic beat Japanese 22-year-old Kurumi Nara 6-4 7-5 while Romanian 11th seed Simona Halep defeated Kazakh qualifier Zarina Diyas 6-1 6-4 to make the second week.