Williams showed no signs of the early-season rust that has plagued many of her main rivals in the early rounds, shooting out to an early 3-0 lead before her 27-year-old opponent, fresh from a triumphant Hopman Cup campaign, threatened to break serve in the fifth game.
The close call sparked the world No1 into action as she claimed the first set in just 29 minutes.
The Spaniard continued to fight, earning a further two break points early in the second set but was unable to capitalise.
Williams made the most of her let-off, claiming the final four games to cruise to a convincing 6-1, 6-2 victory.
“It was a good workout,” Williams said. “It was definitely getting hotter the longer I stayed out, so I needed that. I need to play in the heat as much as I can so it was okay.”
The American will face Vera Dushevina in the next round after the Russian defeated fellow countrywoman Elena Vesnina 6-3, 6-4 to progress to the final eight.
Meanwhile, third seed Svetlana Kuznetsova became the latest big-name casualty to bow out of the tournament after losing in straight sets, 7-6, 6-2, to Slovakia’s Dominika Cibulkova.