The British number one, 27, won a final-set tie-break to edge a finely balanced match.

She joins Katie Boulter and Dan Evans in round two after a 7-6 (7-4) 2-6 7-6 (10-7) win.

Konta will play two-time Grand Slam champion Garbine Muguruza next after the Spaniard beat Saisai Zheng 6-2 6-3.

Konta, who reached a career-high ranking of four in 2017, is left as the nation's leading contender following exits for Andy Murray and Kyle Edmund on Monday.

Now ranked 38th in the world, she showed flashes of the form which helped her reach the 2016 semi-finals in Melbourne in a match which lasted two hours and 51 minutes.

"Overall, every aspect of the match was tough," Konta said.

"I played a tough opponent who I lost to recently [in Brisbane] and the first round of Grand Slams are never easy. And the condition were tough, humid and hot.

"But I competed hard and I'm happy I could compete on every single point.

"I'm happy to have stayed with her when she was playing well but also play tennis on my own terms."

Konta triumphs in topsy-turvy match

Konta's relief was evident as she came through a difficult first-round tie

Konta started the match slowly as she lost serve in the opening game and then looked on the verge of doing the same again as Tomljanovic, 25, threatened to take a 3-0 lead.

But the Briton showed resilience - fighting off four break points - to hold serve in what proved to be a pivotal moment in an enthralling first set.

Serve dominated following those early exchanges until the tie-break when Konta hit a wonderful backhand to bring up two set points, taking the first chance when world number 45 Tomljanovic found the net.

The second set was not as tight on the scoreboard, however.

Konta was left to rue missing a break point in the opening game; going on to lose four straight games as her unforced errors started outnumbering winners under pressure from an inspired Tomljanovic.

Four more opportunities came and went for Konta in a lengthy opening game in the third, but she continued to scrap in the sort of match which has often not gone her way in recent times.

That led to a final-set tie-break - a new initiative introduced when it reaches 6-6 in the decider - with the only previous one at the tournament seeing fellow Briton Boulter prevail in her match on Monday.

Konta's hopes of following suit took a hit when a poorly chosen drop-shot handed early momentum to Tomljanovic, only for Konta to dig deep again and turn the match in her favour.

"I was very conscious to not get excited if I got to seven - I saw Katie Boulter celebrate and thought that would be me," joked Konta when asked about the new format.

"I was thinking 'if you get to seven you haven't won and just keep going'.

"It is different, especially in a singles context, but it is the same for everyone."

Analysis

Russell Fuller, BBC tennis correspondent

Konta's performance in the first set was reminiscent of the form she displayed in Melbourne in 2016 and 2017. Her first serve was landing regularly, and with some potency, and she hit 20 winners as she recovered from a slow start.

Tomljanovic played the better second set, and it looked as if Konta might pay for failing to convert break points when the deciding-set tie-break began.

Konta found herself 6-4 down after developing a sudden addiction to the drop shot but, to her credit, did prove marginally the stronger in an angst-ridden conclusion.