Green's 104 in the second innings of the nine-wicket loss to Bangladesh in Darwin was his first in Australia and also broke an 11-innings run without passing the half-century mark.
The 27-year-old allrounder has been heavily criticised in Australian cricket for not turning his undoubted potential into results.
But his knock against Bangladesh was one of grit and character under immense personal pressure to retain his spot.
Cummins said before the Test that Green had been encouraged to "intimidate" and he did it the way he knows best, driving with commanding power and poise while accumulating runs at a steady rate without taking risks.
It is a method that has worked in Sheffield Shield cricket and he showcased why Test selectors have persevered with him despite the outside noise calling for his head.
Green's third Test century did not lead to a win but that was largely due to the failure of the rest of the order to stay with him in good batting conditions on the third and fourth days.
Australia will consider making changes to their underperforming top-order for the second Test in Mackay that starts on Saturday but Green will be one of the first picked.
"I'm sure he will get an extended run somewhere," Cummins said when asked if Green had tied down the No.5 position.
"I thought he was really impressive and controlled his innings. He looked in total command of his skills. He just needed one or two of us to bat alongside him."
Green struggled in the last Ashes series, as many batters did, making just 171 runs at an average of 24.42 after being moved around from No.5 to No.8. He earlier did a solid job on the tour of West Indies, averaging 30.66 at No.3.
"We obviously think very highly of Cam," Cummins said.
"The last Ashes series probably didn't go as well as he would have liked but before that on the West Indian tour he was probably our best batter in really tough circumstances batting a little higher.
"It was great for him to go out there and show the rest of the world how good he is."
Green was fortunate in the final session on the third day when an inside edge off Taskin Ahmed grazed his leg stump on the way to the boundary.
The bails were not dislodged and the allrounder dug in and made the most of his reprieve.
Green told Fox Cricket after his knock that he has approached his innings against Bangladesh like he used to do "back in the day".
"I think I've just been chopping and changing a little bit recently, so it's nice just to go back to what worked," Green said.
"It has been a long couple of months so it is nice to get a few rewards for it."
As for the critics, Green said it just came with the territory.
"I feel like there are always wolves when you are playing Test cricket. When you play for Australia, you always have to perform," he said.
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