The French Open champion, whose searing backhand is one of tennis's most famous weapons, has not dropped a set in his three opening matches and was untroubled throughout against Verdasco.
The Spaniard, a former top 10 player, looked to be feeling the effects of two punishing five-setters in his opening rounds and came up short at key moments as Wawrinka broke once in each set to clinch victory.
The first set was evenly balanced until the decisive 10th game when Verdasco double-faulted on set point to hand the fourth seed the lead and the second set followed a familiar pattern with Wawrinka breaking for a 5-3 lead before serving out.
Verdasco bravely hung in, but the Swiss, who has never been beyond the quarter-finals at Wimbledon, broke again for a 5-4 lead in the third and finished off the match with his 14th ace.
Next up for Wawrinka will be Belgium's 16th seed David Goffin, who is also yet to drop a set in three matches and polished off Cypriot Marcos Baghdatis 7-6(3) 6-1 6-1.
(Editing by Ed Osmond)
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