Nadal, the tournament's last second seed to lose his opening match in 2006, had no such problems this time as he beat another U.S. player, Taylor Dent, 6-4 6-3.
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The 10 teams preferred by RPI had an abysmal NCAA record, winning just three games, compared to an expected 9.04. (Including one win by New Mexico, as a five seed last year.) Two of those wins were by Northern Iowa, as a nine seed in 2010.
The Kings were the No. 8 seed last season, after all, and the Devils were No. 6 in the East.
The winner of that match will play either fifth seed Petrova or last year's losing finalist, 10th seed Flavia Pennetta of Italy.
Kansas' loss to Michigan on Friday night left Louisville as the last No. 1 seed in the tournament.
Nicholson will hope to continue his form in the last eight against third seed James Wade, who beat Vincent van der Voort 4-0.
Chakvetadze will take on Polish eighth seed Agnieszka Radwanska in the last 16, with the winner to then play either German 17th seed Sabine Lisicki or unseeded Romanian Sorana Cirstea.
The Russian fourth seed's last match was a humiliating straight sets loss to veteran Italian Davide Sanguinetti at the Miami Masters in March.
The Billikens lost in the round of 32 year to No. 1 seed Michigan State last year after snapping a 12-year NCAA tournament drought.
DeQuan Hicks had 12 points for the Demons, who upset Iowa as the No. 14 seed in their last NCAA tournament seven years ago.
Sixth seed Roddick, last weekend's losing finalist, gave home fans some cheer as he crushed Russia's Igor Andreev 6-4 6-4 to set up a clash with Ukraine's Sergiy Stakhovsky.
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In other matches, Maria Sharapova thrashed America's Mallory Burdette 6-1 6-1 to advance to the last 16, while fifth seed Petra Kvitova from Czech Republic beat France's Pauline Parmentier 6-4 6-4.
Seventh seed Jo-Wilfried Tsonga beat Colombian qualifier Santiago Giraldo 6-3 6-4 and will face Ferrer in the last eight, while fifth seed Robin Soderling went down 6-3 6-2 to Stanislas Wawrinka .
The Swiss third seed, whose last major title came in Australia in 2010, had been due to play away from the main Rod Laver Arena court for the first time in 52 matches.
Djokovic, seeking his fourth Miami crown, having also won in 2007 as well as losing the 2009 final, was joined in the last 16 by Spanish third seed David Ferrer, who will next play Japan's No. 13 Kei Nishikori.
The world No. 1 will face fourth seed Novak Djokovic, who reached the last four for the third year in a row after beating Spanish 10th seed Fernando Verdasco in four sets, 7-6 (7-2), 1-6, 7-5, 6-2.
Gasquet, a semifinalist in Miami last month, beat Croatian ninth seed Marin Cilic 7-5 6-4.
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Fourth-seeded Spaniard Montanes moved into the last four by beating Uruguayan eight seed Pablo Cuevas 6-4 6-3.
Japan's Kei Nishikori, the 17th seed also made the last 32 with a 6-2 6-2 6-4 win over home qualifier Tim Smyczek.
In the last four Federer will face sixth seed Andy Roddick , who beat Karol Kucera, conqueror of second seed Juan Carlos Ferrero, 7-6 6-3.
Fourth seed Murray reached the last four in Indian Wells in 2007 and the last 16 a year ago, when world number three Novak Djokovic took the title.
The 28-year-old former world number one will face Egypt's fifth seed Amr Shabana in the last four.
The Swiss will play American 20th seed Sam Querrey in the last 16.
Federer will play unseeded Nicolas Kiefer in the last four after the German beat fifth seed Fernando Gonzalez 7-6 (7-5) 6-2.
In the men's event, Czech second seed Radek Stepanek booked his last four place with a 7-6 6-1 win over American Wayne Odesnik.
His next opponent will be American Ryder Cup captain Tom Lehman, who caused an upset by beating ninth seed Adam Scott at the last.
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