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The 23-time grand slam champion was in fine form at Melbourne Park, where the biggest names in women's tennis were competing across multiple tournaments, as she sealed a straight-sets triumph to continue her preparations for a shot at an eighth Australian Open title.
In doing so the 39 year-old extended her head-to-head record over the Bulgarian to 6-0 and was delighted to get the job done.
"It's definitely nice to get another win," Williams said. "She's clearly a great player, so it wasn't easy, but it was good to come through.
"Last time it was an incredible three-set match, so today I was like, 'All right, let's really try and focus and learn to do better than last time'."
World number one Ash Barty had a less straightforward path to the last eight, requiring three sets to see off Marie Bouzkova.
The home hope ultimately prevailed 6-0 4-6 6-3, with second seed and reigning Australian Open champion Sofia Kenin also taken the distance in a 5-7 7-5 6-2 win over Jessica Pegula, as Nadia Podoroska dug deep to down Petra Kvitova 5-7 6-1 7-6 (9-7).
With Barty now set to face Shelby Rogers, Danielle Collins awaits Williams having impressively defeated third seed Karolina Pliskova 7-6 (7-5) 7-6 (7-3), while Garbine Muguruza overcame Anastasia Pavlyuchenkova 6-1 6-2 to set up a meeting with Kenin.
In the Gippsland Trophy, the top three seeds all dodged upsets, with two-time grand slam winner Simona Halep, 2019 Australian Open victor Naomi Osaka and 2018 Tour Finals champion Elina Svitolina safely navigating through the last 16.
Fifth-seeded Briton Johanna Konta failed to convert two match points as she succumbed to a 4-6 7-6 (12-10) 7-6 (7-4) defeat to Irina-Camelia Begu.
Meanwhile, at the Grampians Trophy there were wins for Anett Kontaveit, Jennifer Brady and Angelique Kerber.