Roddick, seeded fourth in the event, dropped the first set 1-6, edged the stubborn Muller 7-6 (7-2) in the middle set and then put him away 6-2 in the deciding set for the 32nd win of his career.
The former world No. 1 took his other 2012 victory last month at Eastbourne.
Muller, who fell to 1-4 lifetime against Roddick, was done in by 10 double faults.
Attkisson leaves CBS News, reportedly over network's 'liberal bias'
Beautician charged with giving client fatal silicone butt injection