Beaten by nine wickets in the series opener in Darwin in one of Test cricket's greatest upsets, Australia hit back emphatically in Mackay to win by an innings and 51 runs in two days, tying the series 1-1 on Sunday.
The Mackay victory was set up by an incredible opening spell by Mitchell Starc, who took 6-12 in the first innings as Bangladesh were bowled out for 64.
"We needed to bounce back, and it was a great couple of days from the lads," Cummins said.
"I thought everyone was really sharp. You know, it's a bit like the opposite of last week.
"If we get a really good first hour or two, we can set up the rest of the match. I don't expect to get 6-20 or whatever we had every match, but it was a great start. Didn't really let up after that."
Green followed his century in Darwin with a gutsy 67 in the second Test to drive Australia to a 146-run lead, which proved well beyond Bangladesh.
Green's revival followed a lean spell during the Ashes which left former Australia players and pundits questioning the tall all-rounder's place in the Test setup.
"He looked in total command of his batting this whole series," said Cummins.
"So really happy for him. Again, he held our innings together yesterday and this morning. So hopefully, he can take a lot of confidence out of that. We know how good he is.
"Hopefully it continues on."