The 2009 champion and last year's runner-up needed 1 hour, 54 minutes but overcame a slow start, firing nine aces to put away Bulgarian Grigor Dimitrov 7-6 (7-3), 6-3 and reach the Round of 16.
The Briton next faces Italian Andreas Seppi.
He now goes on to face 17th-seeded American Sam Querrey, who won a walkover when Milos Raonic withdrew with illness prior to their third-round match.
No. 6 seed Jo-Wilfried Tsonga of France and ninth-seeded Croatian Marin Cilic will meet in the Round of 16 after each won their Monday matches.
Sixteenth-seeded Andreas Seppi moved on as well with a 7-5, 4-6, 6-2 decision over Brazil's Thomaz Bellucci.
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