Murray, the first player to defend an Olympic singles title, secured his 19th successive victory by a 6-3 6-2 margin.
The 29-year-old, who had a bye in round one, will play South African Kevin Anderson in the third round.
Britain's Johanna Konta also reached the third round with a 6-2 6-3 victory over Donna Vekic and will face fifth seed Agnieszka Radwanska next.
In the men's draw, third seed Rafael Nadal, who won the men's doubles in Rio, beat Uruguay's Pablo Cuevas 6-1 7-6 (7-4). Nadal faces Borna Coric, who defeated Nick Kyrgios, in round three.
Australia's Kyrgios smashed three racquets in one changeover during his 7-6 (7-2) 4-6 7-6 (8-6) defeat by Croatia's Coric.
Switzerland's second seed Stan Wawrinka is also through, beating 18-year-old American wild card Jared Donaldson 2-6 6-3 6-4.
Olympic champion Andy Murray picked up where he left off in Rio by beating Juan Monaco in the Cincinnati Masters.