Tomic managed to win only 10 points in the final set of a 56-minute match dominated by the reigning Olympic and US Open champion, who has a training base in Miami.
"It's very tough conditions," Murray said of his determination to get off to a quick start in his opening match after enjoying a first-round bye.
"You're never going to feel great your first match, especially when it's tricky conditions and with his game style, too," added the Scot.
"I don't know if he was tired or struggling with the humidity, but he was playing pretty low-percentage tennis. That played into my hands."
World No. 3 Murray wasn't sure that Tomic deserved the jeers he heard from fans as he faded in the second set.
"You know, it is tough when you're going behind and making quite a lot of mistakes," Murray said. "I have done it before when my head has gone down and you still want to win, but it doesn't always appear that way."
Murray, who lost to top-ranked Novak Djokovic in last year's final, next faces Grigor Dimitrov, who won the first set against Simone Bolelli with the second set level at 1-1 when the Italian retired with a wrist injury.
Murray, the 2009 Miami champion, beat the rising Bulgarian star to retain his title in Brisbane in January.
The Scot remained perfect in two career matches against Tomic, the youngest player in the ATP top 100 at age 20.
Murray broke in the fifth game and then held serve for a 4-2 lead, taking full advantage of 14 unforced errors in the first six games by Tomic.
Tomic netted a backhand to give Murray a second break, and the first set, in the ninth game of the match.
Murray broke Tomic twice in the second set as well, and closed it out with his eighth ace.
In other men's matches, French sixth seed Jo-Wilfried Tsonga beat Serbia's Viktor Troicki 7-6 (8/6), 6-3 to reach the third round.
World No. 1 Serena Williams continued her progress toward a sixth Miami WTA title with a 6-3, 6-3 third-round victory over Japan's Ayumi Morita.
Williams got off to a slow start, dropping her serve in the second game as Morita raced to a 3-0 lead.
But the American bounced back with a vengeance, winning the next six games to pocket the first set.
She broke Morita for a 4-2 lead in the second, gave herself a first match point with her seventh ace and finished it off with a service winner.
It was good news for the Williams family after elder sister Venus withdrew with a lower back injury shortly before her third-round match against American Sloane Stephens.
"I think it was the right decision for her," Serena said of her sister's withdrawal. "I haven't seen her really on the practice court as much because she wasn't feeling great, so I think she's taking everything a day at a time."
Venus's withdrawal followed that of Australian Open champion Victoria Azarenka on Friday before her opening match with an ankle injury.
Two more top-10 women bowed out on Saturday, as Caroline Wozniacki and Petra Kvitova suffered third-round defeats.
Young Spaniard Garbine Muguruza dispatched ninth-seeded Wozniacki -- a former world No. 1 -- 6-2, 6-4.
Belgian Kirsten Flipkens beat seventh-seeded Kvitova -- a former Wimbledon champion -- 6-0, 4-6, 6-1.
Defending champion Agnieszka Radwanska of Poland, the fourth seed, survived a scare en route to a 7-6 (7/5), 2-6, 6-3 victory over Slovakia's Magdalena Rybarikova.
And fifth-seeded Li Na of China held on for a 6-2, 6-4 victory over American Varvara Lepchenko.