The Russian third seed eventually edged past Frenchwoman Alize Cornet 6-1 7-6 (8-6) in the third round at Rod Laver Arena on Saturday.
Sharapova played the longest women's match of the tournament so far – three hours and 28 minutes – in a tough win over Italian Karin Knapp in the second round.
She admitted to being affected by that long match in her clash against Cornet, which she battled to close out.
"Of course everyone that played a long match in those (hot) conditions is going to feel physically and emotionally tired, and that's the way it goes," Sharapova said.
"You just have to find a way to get through it. That's what I did. It was quite tough in the end.
"She had a set point and she had a chance to level the match out, which is something I probably wouldn't want to do, is go into a third set.
"I was I was happy I was able to finish it in two."
Sharapova has served more double faults (29) – including eight against Cornet – than any player at the Australian Open this year.
But she said there were still positives to take out of her win over Cornet.
"There are definitely things I'm going to have to improve and do better moving forward, because it only is going to get tougher," Sharapova said.
"But I am happy that I took my chances, even though it was pretty close in that second set."
Sharapova holds a 3-2 win-loss record over Cibulkova, but the two have never met on hard-court and last played in 2011.
The Slovakian 20th seed has dropped just nine games on her way to the fourth round and shapes as being a danger.
"She's a great retriever of the ball. It's going to be a very physical match. She likes to make it physical. That's when she plays her best. Obviously I don't want to go there with her," Sharapova said.
"But she's a tough opponent. That's for sure. She plays a lot of top players extremely well and tough and has nothing to lose, so I'm expecting a tough one the next round."