Nadal will face the winner of a later match between French sixth seed Jo-Wilfried Tsonga and German 19th seed Florian Mayer for a berth in the semi-finals of the $9.6 million event.
In an earlier fourth-round match, Serbian ninth seed Janko Tipsarevic beat Bulgaria's Grigor Dimitrov 7-6 (7/3), 6-2.
Tipsarevic will next face the winner of a later match between British fourth seed Andy Murray and French 13th seed Gilles Simon.
The first two women's quarter-finals were also scheduled later with Russian World No. 2 Maria Sharapova to face Chinese eighth seed Li Na and US 10th seed Serena Williams playing Danish fourth seed Caroline Wozniacki.
Rafael Nadal advances to quarter-finals in Miami
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