The French Open holder from Russia, who needed more than three hours to beat qualifier Heather Watson of Britain on Tuesday, showed few signs of fatigue in coming through 6-2, 7-6 (7/5) in the third-round clash.
Six out of eight games in the first set went against serve. Sharapova’s service game had also been a problem against Watson.
“After winning the first set, I was up 3-0 in the second set. I didn’t think it was going into a tie-break,” said Sharapova, 25.
“She had an opportunity to serve out for the second set and I was frustrated in that situation.”
“After the long match yesterday, I’m very happy to be able to win today. I was a little bit down in the second set and I’m just happy to win in two sets,” added Sharapova, winner in Tokyo in 2005 and 2009.
Safarova, ranked 17th against Sharapova’s second in the world, came back from 0-3 down to 3-3 and then 4-4 before hitting a fine service return winner on break point to take a 5-4 lead in the second set.
But again neither could keep their serve in the following three games as the contest went to a tie-break.
Safarova again went down 0-3 in that before coming back to make it 4-4, but made a forehand error twice to give Sharapova a commanding 6-4 lead.
Safarova saved the first match point with an ace, but Sharapova calmly won the match by hitting an ace on her serve.
In the quarter-finals on Thursday, Sharapova will play eighth seed Samantha Stosur of Australia, who defeated Dominika Cibulkova of Slovakia 6-4, 7-5.
On a day of few surprises, defending champion Agnieszka Radwanska of Poland beat qualifier Jamie Hampton of the United States 6-4, 6-3.
Sixth seed Sara Errani of Italy outclassed ninth seed Marion Bartoli of France 3-6, 6-2, 6-2, while fifth seed Angelique Kerber of Germany overwhelmed Urszula Radwanska of Poland 6-1, 6-1.
Nadia Petrova of Russia defeated plucky Petra Martic of Croatia 7-6 (7/2), 6-7 (1/7), 6-4.
When we choose to look away for good, we are as complicit as those at the helm of this atrocity
Over 100 people in Lebanon have been reported killed during the hostilities started on October 7