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Wawrinka won 7-6 (5), 6-2 to extend his winning streak against Nalbandian to four matches, losing only one set in that span.
James Blake defeated Oscar Hernandez 6-3, 6-4 to advance to the second round.
In Madrid, Nalbandian defeated No. 2 Rafael Nadal, No. 3 Novak Djokovic and top-ranked Federer to become only the second player since 1994 to beat the top three players in the same week. Djokovic accomplished the feat earlier this year.
The fourth-seeded Blake is among 20 players seeking to clinch one of the last three spots remaining at the season-ending Masters Cup in Shanghai next month. The American reached the final last year but lost to Federer.
Blake will next face Ivo Karlovic of Croatia.
"That's what I am worried about right now, not the semis or the final," Blake said.
Blake, a wild card in Basel, has to overtake two players to qualify for Shanghai. The Paris Masters next week is the final tournament of the year before the Masters Cup.
If Blake makes the semifinals in Basel, he would move into a tie for eighth place, the last spot for Shanghai.
"I notice it but I don't worry about it," Blake said. "I can't be worried about the other guys, I am just trying to do well at the end of the year."
Hernandez saved one match point on his serve with Blake leading 5-3 in the second set. But Blake went up 40-0 in the next game and closed out the match with a service winner.
Two other players competing for spots at the Masters Cup also advanced. Fifth-seeded Tomas Berdych beat Feliciano Lopez 7-6 (4), 3-6, 6-3 and Guillermo Canas defeated Jose Acasuso 6-4, 6-3.
Also, qualifier Andrey Golubev upset Amer Delic 6-4, 6-3, and Juan Martin Del Potro advanced when Michael Russell retired while trailing 5-2.
Del Potro next faces Federer.
Five players have already qualified for the Masters Cup: Federer, Nadal, Djokovic, Nikolay Davydenko and Andy Roddick.