The ninth-ranked Del Potro controlled the third-round match from the start after breaking Nalbandian, who was coming off a tournament win in Stockholm last week, in the first game.
Del Potro broke again to take the opening set and then seized control of the second with another break in Nalbandian's first service game.
"I have to do my things, but in Davis Cup he is the leader and he is the one that counts above everyone else,'' said Del Potro, who is closing in on a spot at next month's Masters Cup in Shanghai. "I'm getting better day by day. We don't compete to see who is the best from Argentina.''
Nalbandian and Del Potro will play singles for Argentina in the Davis Cup final against Spain from Nov. 21-23 in Mar del Plata, Argentina.
Del Potro's quarterfinal opponent will be the winner of the match between second-ranked Roger Federer, who won here in 2006, and Australian Open finalist Jo-Wilfried Tsonga.
U.S. Open finalist Andy Murray also reached the quarterfinals with a 7-5, 7-6 (2) win over Marian Cilic.
Broken early on, the fourth-ranked Briton broke Cilic to make it 5-5 and again two games later to close out the set.
Cilic rallied late in the next set to force a tiebreaker, but Murray took a 6-1 lead after Cilic double-faulted. Murray clinched the match when Cilic hit a shot long.
"I hit some great shots to break him,'' Murray said. "I was getting chances on his service games. I found a way to get through.''
Murray will next face Gael Monfils after the Frenchman beat the eighth-ranked Andy Roddick 6-4, 3-6, 6-3 on Alcala court.
Gilles Simon of France saved two match points before beating Robby Ginepri of the United States 6-7 (6), 6-4, 7-6 (6). Simon will play either Australian Open champion Novak Djokovic or Croatia's Ivo Karlovic.
Later Thursday, top-ranked Rafael Nadal meets Richard Gasquet of France, with the winner moving on to face Stanislas Wawrinka. The 10th-seeded Swiss player beat Feliciano Lopez of Spain 6-4, 6-4.
De La Red: Sanctions Will Not Affect This Saturday
Nadal, Federer thru to Madrid quarterfinals
