The eighth seeded Verdasco was one of a record seven Spanish players through in the top half of the draw, where Rafael Nadal was the top seed.
The injury-prone but battle-hardened Nalbandian had been expected to give Verdasco, a quarter-finalist here last year, a tough time of it, and so it turned out initially with Verdasco needing eight break points before moving ahead 3-2 in the first set.
The Spaniard tucked away the set 6-2, but quickly fell 0-2 down in the second before breaking back to love in the third game and levelling at 2-2.
Finding his range, Nalbandian grabbed a second break of serve to lead 5-3 and converted a fourth set point in the next game to level the score.
But it was Verdasco who took command in the third set, running off four games in a row from 2-3 down including two breaks of serve.
He then broke Nalbandian again in the third game of the fourth set to lead 3-1 and there was no way back from there for the South American, who was well beaten by the end.
"It was four games and 40 minutes in the first set, but I was feeling good physically all the time and I knew I had to be tough to beat a guy like Nalbandian at this moment," he said.
"The last weeks before here, the results was really tough. It was like tough matches, close matches. Finally I lost all of them.
"So I'm happy how is this tournament going, and I'm getting much more confidence. Winning against Nalbandian who is one of the players in best conditions this summer is gonna help me for my confidence."
Another Spaniard through to the last 16 was 10th seed David Ferrer, who eased past compatriot Daniel Gimeno-Traver 7-6 (7/2), 6-2, 6-2 and his reward is a matchup against Verdasco for a quarter-final spot.
Ferrer, 28, reached the semi-final here in 2007, beating Nadal along the way, but he was in subdued form in the US hardcourt buildup series to New York.
Feliciano Lopez made it three out of three in the first quarter of the draw for the Spanish when his opponent, Sergiy Stakhovsky of Ukraine, abandoned when losing 6-3, 4-0, leaving Nadal to complete the set later against Gilles Simon.
British fourth seed Andy Murray was also in action Sunday with a match against Switzerland's Stanislas Wawrinka, whom he defeated in straight sets two years ago en route to the final.
American hopes, following the defeats of Andy Roddick and James Blake, lay largely with twin giants Sam Querrey and John Isner.
Querrey delivered in style with a stunning 6-3, 6-4, 6-4 win over 14th seed Nicolas Almagro of Spain.
"Hopefully we got someone who can win a grand slam - John and Mardy (Fish) and myself - we got a chance," he said of the possibility of a first US winner in New York since Roddick in 2003.
"I feel like I am playing the best I've played all summer."
The American, at 22 the youngest player left in the tournament, was untouchable on his own serve and, more suprisingly, he more than matched claycourt specialist Almagro in the extended exchanges.
Isner, the tallest player in the men's draw at 2.05m, was scheduled for the night session on the Arthur Ashe Centre Court against tough Russian Mikhail Youzhny.
Men's Results
David Ferrer (10), Spain, def. Daniel Gimeno-Traver, Spain, 7-6 (2), 6-2, 6-2.
Fernando Verdasco (8), Spain, def. David Nalbandian (31), Argentina, 6-2, 3-6, 6-3, 6-2.
Sam Querrey (20), United States, def. Nicolas Almagro (14), Spain, 6-3, 6-4, 6-4.
Feliciano Lopez (23), Spain, def. Sergiy Stakhovsky, Ukraine, 6-3, 4-0, retired.