Slovenia-born Bedene received loud support on a sun-baked Court Two but could make little impression against the 34-year-old grasscourt specialist who won 7-6(4) 7-5 6-4.
Bedene was one of four British players to reach the third round - the most for 20 years.
Muller treated the crowd to sublime serve and volley tennis and won 82 percent of points on his first serve, fully justifying being bumped up from 26th in the rankings to the 16th seed for the men's singles.
He has played 13 sets of singles and doubles in three days, including his five-set win over Lukas Rosol in the previous round, but will now get the weekend off before a possible fourth round showdown with Rafa Nadal.
(Reporting by Martyn Herman; Editing by Louise Ireland)
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