The win sees the Lions clich the series 2-0 with the third and final test in Sydney on Saturday.
The Lions trailed 23-5 after 30 minutes following Wallaby tries from James Slipper, Jake Gordon, and Tom Wright, with Dan Sheehan responding for the tourists. However, important scores from Tom Curry and Huw Jones closed the gap to 23-17 at halftime.
In a tense second half, Tadhg Beirne's converted try brought the Lions within two points before Hugo Keenan dived over in the 79th minute for the match-winner. A controversial TMO check cleared Jac Morgan's ruck clear-out in the build-up, allowing the try to stand.
Huw Jones was set to miss all the drama after initially being left out of the starting XV, despite having impressed in the Suncorp Stadium opener.
But having been dropped for Garry Ringrose, he was reinstated at outside centre when the Irishman self-reported a return of the concussion symptoms that had ruled him out of the first Test.
"It was a pretty mental week. I had the initial disappointment of not being in the squad on the Tuesday," Jones said after the game.
"I had a chat with Andy (Farrell) and I was gutted. I got over that and was ready to get behind the boys.
"And then on Thursday we trained and Garry - to be fair to him - said his head just wasn't right. I think he may have got a knock in the session and went to the doctor.
"That's brave. And pulling yourself out as well. It was at the end of training, I had no idea that he was struggling,
"I chatted to Garry afterwards and he was emotional. Its one of those... you think 'I'll be all right' but if it's bad, it's bad.
"But like people have said, it's just a game. Your head's very important, you only get one brain and all that.
"If he felt the need to say that he was struggling, then fair play to him. I just hope that he gets over it very quickly.
"I was gutted for him because he deserved to play and I know he would have been unbelievable. Sometimes that's rugby and that's sport.
"So I got a nod after that session. I was ready to step in and luckily I'd run some of the plays on Tuesday, so I was ready to go and got the job done."
Jones played a key part in the Lions' comeback when he powered over just before half-time.
Keenan's try was the first time the Lions had led in the second Test.
"What a game. Unbelievable. We made it hard for ourselves, ill-discipline and all that, but came back at the end and Hugo... what a finish. It was a good feeling," Jones added.
"It's a cliche, but we never stopped believing, even at half-time. Even if we'd been further down, we still had the belief that we'd go on and win."