Verdasco, seeded 31st, had lost 13 of 14 prior matches with the Scot, who claimed the first of his three Grand Slam titles at the 2012 US Open.
But on another scorching day in New York, Verdasco triumphed 7-5, 2-6, 6-4, 6-4 to book a third-round meeting with another former champion, third-seeded Argentine Juan Martin del Potro.
"I only beat him in the Australian Open 2009, so the only time I beat him was a Grand Slam, so it was a little bit of motivation to come here today and try to beat him again," Verdasco said.
Murray was playing his first Grand Slam since Wimbledon of last year after battling a hip injury that required surgery in January.
He returned to the major stage with a four-set win over Australian James Duckworth on Monday, but he didn't have enough to withstand 52 winners from Verdasco.
Murray made the Spaniard work to close it out, Verdasco saving five break points in the final game before converting his third match point.
"It was tough of course to close the match but I think with Andy it's always tough -- not to close it just to play every point because he's an unbelievable fighter," Verdasco said.
"Even with all the surgery and not 100% physically he's a fighter."