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The two-time Grand Slam champion, who was stopped at the quarter-final stage in the last two Wimbledon Championships, was beaten 6-2 7-6(3) by Verdasco on a rain-affected day in London.
It was a troubling start for Wawrinka as he lost his opening service game, which immediately put him on the back foot.
The Swiss player squandered six break points in the first set as Verdasco took a one-set lead in 38 minutes, but it was more competitive in the second set.
Just three break points were created in 13 games as both were strong on serve, but Verdasco stepped up in the tie-break as he nabbed it 7-3 to book a spot in the second round.
Wawrinka was competing for the first time since losing to Andy Murray in the semi-finals of the French Open earlier this month.