Murray recovered from a poor first set and survived two break points when he served for the match to beat Argentinian qualifier Juan Ignacio Londero 2-6 6-2 6-3.
Murray, who won back-to-back matches for the first time since his return in Beijing last week, will play Italy's Fabio Fognini in round two.
The Scot can expect to face a much sterner test against the 10th seed, after a series of forehand errors saw him slip to an early deficit against world number 289 Londero.
The Argentinian converted two of five break point opportunities in the opening set and held off all three on his own serve, to take a commanding lead.
Murray's expectations were clear in the way he vocally and visibly expressed his frustration after struggling to make the desired impression.
But the Scot was much improved in the second as he returned the favour, breaking his increasingly vocal opponent twice while not allowing him any openings on his own serve.
Murray squandered an early advantage in the deciding set when, having broken Londero to love to establish a 3-1 lead, he was immediately broken back.
But Murray let out a roar after claiming the third consecutive break and he would hold on for the win, despite falling 15-40 down when he served for the match.