The Briton faced 13 break points in the first set and struggled with her rhythm as the big-hitting Tomljanovic stormed into an early lead.
Konta, who had similar struggles with her serve in her opening match against American Madison Keys, a U.S. Open finalist, on Monday, responded with a better performance to level the contest.
The world number nine raced to a 5-2 lead in the deciding set before Tomljanovic showed signs of fighting back. However, Konta held on to finish the job.
"She made that very difficult, so that's a credit to her and she played incredibly freely at the end of the third set," Konta said after the match. "There wasn't a lot in it so I'm very happy to have just stayed tough and just come through that.
"To be honest, it's a great thing to have two tough matches early on. It's a boost, the match fitness, and it boosts a lot of the competitive scenarios that we're going to face the whole year. I'm sure my next match will be the same."
Muguruza's wretched run of injury problems at Brisbane extended to a fourth consecutive year with the Spaniard unable to continue while leading 2-1 in the deciding third set against Serbia's Aleksandra Krunic.
Meanwhile, France's Alize Cornet defeated Croatia's Mirjana Lucic-Baroni 6-1 7-5 to move into the quarter-finals and was joined by seventh seed Anastasija Sevastova of Latvia who beat Romania's Sorana Cirstea 6-2 6-1.
(Reporting by Shrivathsa Sridhar in Bengaluru Editing by Jeremy Gaunt)
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