Williams won 72 percent of her first-serve points, and she piled up 17 break points, converting 11 of them.
Her quarterfinal opponent will be fifth-seeded Simona Halep of Romania, who advanced when the Czech Republic's Barbora Strycova retired while trailing 6-3, 1-0. Strycova was dealing with an upper-respiratory illness.
Third-seeded Agnieszka Radwanska of Poland defeated 19th-seeded Jelena Jankovic of Serbia 6-3, 6-3 to advance to the quarters. Radwanska will meet eighth-seeded Petra Kvitova of the Czech Republic, who rallied to beat American qualifier Nicole Gibbs 4-6, 6-3, 6-4.
Nadal, seeded fourth, rolled through the first set with help from five Verdasco double faults. The second set featured four service breaks before Nadal emerged with a win in a 20-point tiebreaker.
Tiebreakers also were the key as Kei Nishikori won his third-round match. The fifth-seeded Japanese player edged American Steve Johnson 7-6 (6), 7-6 (5).
Ninth-seeded John Isner also sealed his victory in a tiebreaker, topping France's Adrian Mannarino 6-4, 7-6 (4).
The longest tiebreaker of the day went the way of a player who lost his match. Fourteenth-seeded Roberto Baustista Agut of Spain fell 7-6 (5), 6-7 (10), 6-4 to 18th-seeded Feliciano Lopez of Spain.
Germany's Alexander Zverev knocked off 16th-seeded Gilles Simon of France 6-2, 6-2, while 11th-seeded Dominic Thiem of Austria topped 21st-seeded American Jack Sock 7-5, 6-7 (5), 6-1.