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Russell, a 33-year-old who lives in Houston, converted five of his break point chances against the world number nine to triumph in 74 minutes.
It was Russell's first victory over a top-10 opponent in 13 attempts.
Russell booked his first tour-level quarter-final of 2012. He'll face 19-year-old fellow American Ryan Harrison, a 6-2, 6-4 winner over Russian Igor Kunitsyn.
Second-seeded John Isner, playing his opening match after a first-round bye, rallied to beat Horacio Zeballos of Argentina 6-7 (3/7), 6-4, 6-2.
Isner arrived in Houston from Monte Carlo, where he led America to a Davis Cup triumph in France last weekend. He won both of his singles matches in the United States' 3-2 victory in the quarter-finals of the nations tournament.
On Thursday the 26-year-old didn't drop his serve and fired 16 aces in the match lasting two hours and 13 minutes.
Isner, ranked 10th in the world, is seeking a first career clay court title. He next faces defending champion Ryan Sweeting, A 6-3, 6-2 winner over fellow American Bobby Reynolds.
Fifth seed Kevin Anderson of South Africa defeated American Sam Querrey 7-6 (7/3), 3-6, 7-6 (7/2) to reach the quarter-finals.
Anderson, seeking to add a second title of 2012 to the one he captured at Delray Beach last month, next faces fourth-seeded Juan Monaco of Argentina. Monaco defeated Japan's Tatsuma Ito 6-3, 6-3.
Monaco, who claimed his fourth career title at Vina del Mar this year and was a semi-finalist at the Miami Masters, is through to his third quarter-final of the year.
The other quarter-final match-up was determined on Wednesday, with third-seeded Feliciano Lopez of Spain advancing to a clash with sixth-seeded Carlos Berlocq of Argentina.
