Zac celebrated his birthday with a star-studded group of friends, including Chris and Liam Hemsworth's dad Craig, tennis pro Pat Rafter, radio host Kyle Sandilands and 'The Voice Australia' host Renée Bargh.
The news comes after it was recently reported that Vanessa has helped "calm" Zac down since they started dating after they met in Australia in June.
An insider said: "Zac and Vanessa are really good for each other. She has calmed him down a lot, and he's not partying too much."
Instead of partying, the couple much prefer to spend their time exploring nature.
The source added: "Vanessa loves to be active. She and Zac have that in common."
Zac infamously had a wild streak after finding fame in the Disney Channel franchise 'High School Musical', but after seeking treatment for issues with alcohol and cocaine in early 2013, he has been sober ever since.
Speaking in 2014, he said: "I just started going [to Alcoholics Anonymous meetings]. And I think it's changed my life. I'm much more comfortable in my own skin. Things are so much easier now. It's a never-ending struggle."
Meanwhile, the 'Greatest Showman' star was said to be "having fun" Down Under with his new beau, after they met when she was working at the Byron Bay General Store & Cafe.
A source said: "Zac met Ness earlier in the summer. They started hanging out in July and recently took a ski trip together.
"You can tell that they are having fun. She spends a lot of time at this house."
