The Russian fourth seed, who won the 2004 title, has yet to drop a set but came through what was by far her longest match of the tournament in the 97-minute contest on the 11,000-seater Court One.
She faces Coco Vandeweghe in Tuesday’s quarter-finals after the US world number 47 knocked out Czech sixth seed Lucie Safarova, last month’s beaten French Open finalist, their fourth round encounter.
Sharapova had a nervy start against world number 34 Diyas and was 3-1 down in the second set but the 28-year-old’s experience told and she looked delighted at the end.
“The further you go, the tougher it gets. My opponent is a really good grasscourt player, stayed really low and hit so hard so I really had to be ready for all her shots,” Sharapova said.
“Coming into this tournament, I didn’t have a warm-up event and I wanted to start off strong and give a good chance for myself.
“I thought I’ve been doing good but as we all know, it only gets tougher from here.
“It’s a great position to be in. I lost at this stage last year so was extremely happy to go a round further and continue.”
The Siberian won Wimbledon 11 years ago but has only made it past the fourth round once since 2006.
Sharapova is one of just three top 12 players left in the tournament along with world number one Serena Williams and fifth seed Caroline Wozniacki. -AFP