The Spaniard, who had heavy strapping on both knees, needed treatment for tendonitis during the match.
Jones, the world number 123, was a break up in the third set before Nadal roared back to win 7-5 3-6 6-4 6-1.
World number one Roger Federer beat Chile's Paul Capdeville 6-1 6-4 6-4 in Wednesday's late match.
"I'm very happy the way I played. I think I hit the ball well," said Federer, who made just 11 unforced errors in the match.
World number two Nadal said: "Maybe in another tournament I never go to the court today, but it is US Open and it is very important to me.
"I have more than one day now and I hope it will improve. It's tough when you can't play at 100% in a very important tournament like this.
"But for me, the tournament is not finished. I'm still there."
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