Nalbandian improved to 3-0 against Cilic, including a semifinal victory in Washington in August, which he won when ranked 117th and returning from injury. A sore left hamstring followed a 10-month absence after hip surgery.
"It was a very strange year," said Nalbandian, who turns 29 on Jan. 1 and has been out of the top 10 since February 2009. "That is one of the goals for next year. I'm just trying to play as well as I can."
Story continues below ↓advertisement | your ad hereThe 29th-ranked Argentine mixed accurate serving and strong groundstrokes against Cilic, clinching the win on his first match point with a powerful forehand.
Nalbandian, the 2002 Basel champion and a three-time runner-up, next faces either fourth-seeded Andy Roddick of the United States or Andrey Golubev of Kazakhstan, who played later Thursday.
Czech wild card Radek Stepanek earned a quarterfinal match against Roger Federer by beating Santiago Giraldo of Colombia 3-6, 6-2, 6-0.
Richard Gasquet of France won 6-4, 7-5 against Germany's Tobias Kamke, a lucky loser in qualifying who eliminated third-seeded Tomas Berdych in the first round.
Gasquet has a last-eight match against Viktor Troicki of Serbia, who got a walkover win when Frenchman Paul-Henri Mathieu withdrew citing a knee injury.
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