Carballes Baena was lethal from the baseline and fired off seven aces as his Danish rival struggled to make any form of impact on a muggy afternoon match at Flushing Meadows.
Rune suffered early exits from tune-up events in Toronto and Cincinnati and there were early signs of trouble on Monday as he failed to earn a break point in the first set.
Carballes Baena converted on break-point chances in the fifth and ninth games but his serve lost its firepower in the second set, where Rune finally broke in the third game.
The Spaniard, who won in Marrakech earlier this year, cleaned up his act in the third set, where he broke Rune to love in the eighth game, and had clear control over the affair in the fourth set, where he only dropped a single first-serve point.
Carballes Baena broke his opponent's serve in the third and seventh games and beamed widely after Rune surrendered the match with an unforced forehand error.
