Duque-Mariño was feeling very comfortable on these courts, having already played four matches this week - she got into the draw as a lucky loser. But the No.1-seeded Sharapova was just too sharp from start to finish, needing just 68 minutes to complete the victory in front of her adoring fans, 6-1, 6-2.
"The goal is to get better and improve as I go further in the tournament," Sharapova said.
"The day before yesterday in my first match I had to make some little adjustments while I was playing, but today I really felt better. In the end it got a little bit tough - I got broken back a couple of times - but overall I'm very happy with the way that I played tonight. I felt pretty solid out there."
Sharapova was asked about the atmosphere on the court and the strong fan support she had.
"I really enjoyed the atmosphere," she said. "When the crowd gets into the match and they're being supportive of both players it's extremely important to feed off their energy, because as athletes I think we always perform better when we feel the atmosphere from the music and people cheering.
"I think having that kind of atmosphere out there really helps us lift our games."
Sharapova is playing the 19th International-level event of her career, and she has now reached the quarterfinals or better at 18 of them. The only pre-quarterfinal loss? It came at Tokyo [Japan Open] in 2002, her first year on the tour. She lost in the first round to Emmanuelle Gagliardi that week.
Standing between Sharapova and the semifinals will be Magdalena Rybarikova, who put together one of the best serving performances in recent memory - as well as some fantastic returning - to cruise past Elena Bogdan in 44 minutes, 6-0, 6-2. Rybarikova lost just two points in seven service games - she won 28 of her 30 service points - and she broke the Romanian qualifier five times in the match.
Sharapova and Rybarikova will be playing against each other for the first time.
There was a big surprise a little later on at night as WTA Rising Star Monica Puig stunned the No.2 seed, Sara Errani, 6-1, 6-1. Puig had beaten Errani in straight sets in their only other previous meeting as well, in the first round of Wimbledon two years ago - that one was by a 6-3, 6-2 scoreline.
The other two seeds in action moved safely into the last eight, with No.3 seed Caroline Garcia beating Bethanie Mattek-Sands, 6-2, 6-3, and No.5 seed Timea Bacsinszky beating Lesia Tsurenko, 6-2, 7-6(4). Mirjana Lucic-Baroni, Johanna Larsson and Sesil Karatantcheva also moved through.