The 28-year-old, who took over two hours and 30 minutes to beat Tomic, will take on David Ferrer in the quarter-finals.
The British number one impressed from the off as he went a break up at the first time of asking before moving into a 2-1 lead, but Tomic managed to break back to draw level.
Murray responded immediately, though, as he went on to snatch serve twice, and despite going another break down, it was not enough to change the course of the set and he took the lead on the Rod Laver Arena.
Both players failed to hold their opening service games in the second set, but Murray edged ahead by going a break up, taking a 2-1 lead in the set.
Tomic struggled to bounce back as he could not muster a single break point after losing serve in the third game, and it was a comfortable set for Murray.
The Brit looked on course to wrap up the third set swiftly when he converted an early break point, but Tomic kept himself in contention by instantly breaking back.
A tie-break was eventually needed to decide the third set, and Murray started well by moving into a 3-1 lead before wrapping it up 7-4.