The second seed, who was forced to save match-points against fellow Russian Alexandra Panova in the second round, was impressive against Diyas completely destryoying her from the baseline.
Sharapova hammered 22 winners past the hapless 31st seed.
"I think I rebounded really well. I had a good hit yesterday," Sharapova told reporters after the match.
"Just kind of thought a little bit about what I wanted to try to achieve tonight no matter who I played.
"Of course, I focused a little bit on myself more than anything else.
"Just tried to be a bit more aggressive, concentrate. I thought I did a good job of focusing well," she added.
She will next play China's Peng Shuai for a place in the quarter-finals.