Tomic didn't have everything go his way but did enough to progress in straight sets with a 7-5 7-6 (7-3) victory to set up a clash with Murray on Saturday.
Murray, who enjoyed a first round bye in Miami, emerged victorious in the only previous match between the two - a 6-3 6-2 win in Brisbane last year.
Meanwhile, China's Li Na made a winning return to WTA action on Thursday, beating Kiki Bertens of the Netherlands 6-3 6-1 in her second-round opener at Miami.
Li had been sidelined for seven seeks after hurting her left ankle in the final of the Australian Open, where she fell to Victoria Azarenka.
"I wasn't nervous today before the match, but I was excited," Li said.
"For the last six or seven weeks I haven't played any tournaments so I was happy with the result and to win my first match after such a long time."
Li, ranked fifth in the world and seeded fifth in a field headed by world No. 1 Serena Williams, didn't drop her serve, saving both break points she faced in the emphatic 67-minute match.
She was buoyed by a vocal contingent of fans, something she wasn't expecting.
"There were a lot of fans there to support me today, I was like 'Wow!'" she said.
"My game was pretty good. I followed the plan of what I should do. I just had to believe in myself that I could do it."