Blake, who has won two matches at an ATP event for only the second time this year, has risen from 173rd to 90th in the rankings since March. The 31-year-old American will face German Tobias Kamke or countryman John Isner next.
Argentina's Nalbandian, a former World No. 3, has slid to 27th after surgery earlier this year to repair a hernia and torn left leg muscle. He managed to connect on only 49 percent of his first serves in Tuesday's match.
Blake broke in the second and fourth games of the first set and again to open the second set.
He denied Nalbandian on two break points in the first set and another in the first game of the second set on his way to winning after 72 minutes, the final point coming when Nalbandian netted a forehand.
India's Somdev Devvarman, the reigning Commonwealth Games and Asian Games champion, advanced to the second round by beating Germany's Denis Gremelmayr 6-2, 6-3.
Devvarman, a 26-year-old who last week was ranked a career-best 62nd in the world, will next face seventh-seeded Cypriot Marcos Baghdatis, last year's Washington runner-up.
American Ryan Sweeting put himself into the path of French top seed Gael Monfils with a first-round triumph.
Sweeting ousted countryman Alex Bogomolov 6-2, 6-4 in the first round of the US Open hardcourt tuneup event to reach a second-round date Wednesday against seventh-ranked Monfils, among 16 players to receive an opening-round bye.
"Definitely the fastest person I've seen in most sports," said Sweeting. "I'm going to have to play well and stay aggressive. It's going to be a tough match. If I hit a great shot, I've got to expect it's coming back at me.
"If I just sit back, he's going to run for days and make me look like an idiot."
Sweeting captured his first ATP title last April, winning the US Clay Court Championships at Houston, and found his serving rhythm after troubles all year.
"I was seeing the ball well," he said. "I served well. I have been working on my serve a lot. I have been struggling with it all year."
US wildcard Ryan Harrison defeated Germany's Mischa Zverev 6-4, 1-6, 6-1 to book a second-round date with Serbian third seed Viktor Troicki. Harrison is among a hungry set of young US players with something to prove.
"The US work ethic is back," Harrison said. "Some of the American guys are working hard to maximize their potential. We know what people say about Americans, that we are lazy, and we're out to prove that it's not true."
Chilean Fernando Gonzalez pulled out with knee tendinitis and was replaced by Bosnian Amer Delic barely 90 minutes before a first-round match with German Tommy Haas, who advanced 6-2, 6-3, in his continuing comeback from hip surgery.
"The movement and confidence is still not where I would like it," former World No. 2 Haas said. "I don't know where I'm at with my game still."
What the stars mean:
★ Poor ★ ★ Promising ★★★ Good ★★★★ Very good ★★★★★ Exceptional