Unforced errors meant Muguruza's serve was broken in the first game of the match as Tomljanovic raced into a 2-0 lead on Friday, reports Efe.
The Spaniard then unleashed her strong two-handed backhand and her powerful drive as she walked away with the first set 6-3, producing 11 winners.
The second set was even more lopsided, as world number three Muguruza broke her opponent in three consecutive games, winning the set 6-0.
She moves on to the semi-finals, where she will face Romania's Ana Bogdan, who won her tie against American Danielle Collins 6-2, 6-4.
Olympic champion Monica Puig of Puerto Rico lost in straight sets to fourth-seed Hungarian Timea Babos.
Elsewhere in the quarter-finals, seventh-seed Sachia Vickery of the United States defeated the Slovak Magdalena Rybarikova 6-0, 6-3.
(This story has not been edited by Social News XYZ staff and is auto-generated from a syndicated feed.)
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