Ali is under pressure to keep his spot in England's side ahead of rookie Mason Crane, after taking just three wickets at 135 for the series and failing to spin England to victory in Melbourne.
A notable all-rounder, Ali has managed to average just 19.42 batting in the top seven for England after a side strain struck him down in warm-up matches and he later battled a cut finger.
Ali, 30, has also drawn criticism from English spinning predecessor Graeme Swann and former captain Michael Vaughan in recent days.
But when asked whether Ali was still in England's best XI on touching down in Sydney, Bairstow bit back at the criticism.
"A guy who is the second-fastest [England player] ever to 2,000 Test runs and 100 Test wickets. I think that that's unquestionable to even think he's not in our best XI," Bairstow said.
"He wouldn't have played the first four Test matches if he's not in that first XI. There aren't many finger spinners who will come to Australia and bowl teams out.
"It's very important that you get behind Moeen. He can take a game away from you.
"And I think that's something that whether it's this game or the first Test match in New Zealand [in February], the talent and the capabilities of Moeen Ali are unquestionable."
Bairstow's comments come after England's most successful captain, Vaughan, said Ali could no longer command his spot as an allrounder based on his bowling.
"Moeen Ali, to get in this England Test team going forward, has to be in the top five — and if he can't be in the top five as a batsman, I don't see how he gets in the side," Vaughan told the BBC.
"England need to find the next best spinner to come into the Test team.
"And Moeen Ali, to be a regular in this Test team it can't be that he bats at number eight. It can't be that he bats and bowls a bit."
Vaughan also called for 20-year-old Crane to replace Ali for the Sydney Test.
"For me he has to play in Sydney, because of what we've seen in Moeen Ali," he said.
"I didn't agree with [his spot in the squad originally], but you have to get him in for Sydney because I don't see how he can do any worse than Moeen.
"It's probably doing the right thing for Moeen leaving him out — he just looks shot to me."