French third seed Muller, positioned at 32nd in the ATP rankings, followed his title win at Hertogenbosch last year with a run to the Wimbledon quarter-finals.
Australian Bernard Tomic, a Wimbledon quarter-finalist in 2011, recorded his first win against a top-50 player since last June as he beat sixth-seeded Dutchman Robin Haase 6-3 7-5 to advance to the last eight.
Tomic, ranked 181st in the world, will face fourth-seed Fernando Verdasco in the next stage after the Spaniard ousted Russian Daniil Medvedev 6-4 6-1.
Verdasco will be hoping to end his winless streak against Tomic, who has come out on top in their last five meetings.
Frenchmen Adrian Mannarino and Richard Gasquet, the top two seeds of the tournament, will play their second-round matches against compatriot Jeremy Chardy and Russian Evgeny Donskoy respectively on Thursday.
(Reporting by Aditi Prakash in Bengaluru, editing by Ed Osmond)
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