The US Open champion got through the match thanks to some excellent serving and a couple of loose games from his opponent, winning 6-4, 3-6, 7-6(1).
Verdasco once again found himself on the losing end having been the better player for most of the match, just as he did in his first match at LondonÃ¢â‚¬â„¢s O2 arena against Roger Federer.
The Spaniard, who has enjoyed a breakthrough year in his career after a momentous Davis Cup final victory against ArgentinaÃ¢â‚¬â„¢s Jose Acasuso at the end of 2008, was the aggressor for much of the match, unleashing his powerful forehand as a rival to del PotroÃ¢â‚¬â„¢s major weapon.
But Verdasco still seems to lack that mental fortitude at times, which is perhaps why he has remained in the bottom half of the top ten rather than mounting a real challenge on the big four of Roger Federer, Rafael Nadal, Novak Djokovic and Andy Murray.
An error-filled service game cost him the opening set, but he fought back in the second, matching his strikepower with consistency. The third set looked like it would be a repeat of the first, when Verdasco once again found the wrong side of the lines in the eighth game.
But del Potro wobbled when serving for the set and Verdasco was able to take the match into a deciding third set tiebreak, although only after saving match points on his own serve.
The breathtaking power and accuracy that had got him to the shootout then deserted him and del Potro moved up a gear to wrap up the tiebreak 7-1.
Earlier in the day, third seeded doubles pair Mahesh Bhupati and Mark Knowles recovered from a set down against Polish duo Mariusz Frystenberg and Marcin Matkowski, who have already been the scourge of world number ones Daniel Nestor and Nenad Zimonjic.
The Indian-Bahamian team eventually came through in the match tiebreak, 3-6, 6-3, 10-7.
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BIOGRAPHY: Marcus Rashford