Woakes kept his nerve in a tense finale to hit the winning run from the final ball, sealing a record eighth consecutive Twenty20 success by a single wicket.England had looked on course to complete a comfortable pursuit of Australia's 157 for four before four late wickets from Shane Watson, who finished with a career-best four for 15, left them teetering.
The tourists needed four runs from five balls when last man Ajmal Shahzad joined Woakes at the crease.
Shahzad took three balls to scramble a single but, with the game seemingly slipping away, Woakes levelled the scores with a cut for two before lofting a drive from the final ball to win the match.
"It was a fantastic performance by him. To be honest I hadn't seen much of his batting, but [team director] Andy Flower said he was a serious batter," said captain Collingwood.
"You never know what you are getting with new players but I thought he responded really well on debut and put in a great performance. He looks a serious batter as well, you can say he's a true all-rounder.
"To have a youngster come in a lead us home like that was great, [but] I don't think we should be leaving it up to him."
England had threatened to throw the match away as they lost four wickets for 24 after Eoin Morgan's classy 43 ensured they remained in front of the required rate.
But when Morgan fell to Watson the wickets tumbled and Collingwood admitted his team had been lucky to escape in the end.
"It was a great game. I thought it had everything," he said.
"There was some proper, serious batting throughout the game and at the end we should have seen it through a little easier but Twenty20 cricket can get a little bit like that at the end.
"I'm delighted with the record as well, it's a huge achievement for the team."
Collingwood described England's record run of eight wins, which began during their World Twenty20 success in May last year, as "very special" and believes it is a feat that could go unbroken for some while.
"It means a lot. It's a world record. We always say we want to create history, it's a new form of the game but, let me tell you, eight wins in this form of the game is something very special.
"It only takes one performance to take it away from you like Shane Watson nearly did tonight. I can't see many teams getting close to that in the future."
New Australia Twenty20 captain Cameron White was left disappointed to miss out on victory on his first night in charge.
The defeat continued a miserable run for Australia this winter, but White believes his side can claim a much-needed win in the final game of the brief Twenty20 series in Melbourne on Friday.
"It was an interesting first night for me. It just seems to be the way it is rolling at the moment," he said.
"It's up to us in Melbourne to try and turn it around. There's probably a few things in Melbourne we can try and do to do that.
"When England needed a big shot or a boundary they just seemed to find it. Whether that was good batting by England or just a bit of mis-execution from us, I'm not sure. We'll have to have a chat about that."
White also praised the performance of Watson, who had blasted 59 from 31 balls at the top of the order before almost snatching the game away with the ball.
"[It was] a class act, wasn't it? He just showed his all-round ability and what a good cricketer he is.
"He's destructive with the bat and his execution with the ball was exactly what the team and myself was asking for. It was a very classy display I thought."
