Verdasco, who stunned the 14-times grand slam champion in a five-set epic, won the opening set against the Israeli but faded to lose 4-6 6-3 6-3 7-6(4).
The Spaniard looked fatigued from his exploits against Nadal while the diminutive Sela, cheered on by a flag-waving contingent of fans, struggled with nerves near the end.
Verdasco's cause was not helped by consecutive double-faults in the fourth set tiebreak, gifting Sela a 5-2 lead.
He managed to save a match point but finished the job with a well-struck backhand return that Verdasco netted.
Sela, 30, will now play Frenchman Jeremy Chardy or Russian Andrey Kuznetsov for a place in the fourth round of a grand slam for only the second time in his career.
(Reporting by Martyn Herman in London. Editing by Patrick Johnston)
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