WA were in trouble at 7-53 in their second dig ahead of lunch on day four, still trailing the hosts by 26 runs overall.
However, talented young gun Green - backing up from his impressive 87 not out in the first innings - again stood tall, striking an unbeaten 121 batting at No.9 as WA finished at 9-246 with an overall lead of 167.
First he shared a 115-run eighth wicket stand with nightwatchman Matthew Kelly who survived 180 deliveries for his 46 runs.
Then he dug deep with number 10 Jhye Richardson (21), combining for a 52-run partnership.
The 20-year-old said it was an innings he'll never forget.
"I'm really happy to have helped the team come away with a draw when we easily could have fallen short," Green said.
"It was nice to give my dad a call at the end of the day and tell him how I went.
"I was pretty emotional speaking to dad, I've spent a lot of time with him down at the cricket nets when no one's watching.
"For all that hard work to pay off and score my first century was special."
In the end Queensland agreed to a draw with 20 overs for the day still remaining, finally relenting to Green's remarkable resistance.
"At 7-53 we looked dead and buried, but we have something special in Cameron Green," WA captain Shaun Marsh said.
"He certainly has a bright future for not only WA but Australia."
Western Australia head to Sydney later this week to take on New South Wales in their next Sheffield Shield match, starting Monday 11 November at the SCG.