With the scores level at 157 runs each, Woakes smacked the ball over mid-wicket to extend the world champions' winning run in the shortest form for the game to a record eight matches.
"Eight wins in this form of the game is very special," England captain Paul Collingwood [ Images ] told reporters.
"It was a great game of cricket, it had everything. I thought we probably should have seen it through a little bit easier, but Twenty20 cricket can get a little bit like that towards the end."
Australia's Shane Watson [ Images ] took four for 15, including two wickets in two balls, and made 59 of 31 balls with the bat, including three successive sixes and 26 in total off Graeme Swann's [ Images ] first over.
It was all in a losing cause for the Test opener, however, as England's tail overhauled a modest target in front of 32,000 fans at the Adelaide Oval desperate for a measure of revenge after Australia's Ashes drubbing.
"It was very disappointing not to get over the line," said Watson. "It doesn't matter how I played as an individual, the important thing was the win for the team and unfortunately we got close, it wasn't good enough."
The evening might have been different had Australia's Stephen O'Keefe not dropped Ian Bell [ Images ] off the first ball of England's innings, the in-form batsman going on to make 27 as the tourists made a brisk start.
Michael Yardy was bowled for a duck first ball to leave England 28 runs from victory with three wickets in hand and Watson on a hat-trick.
Woakes denied him but Australia were celebrating again when Brett Lee [ Images ] caught Tim Bresnan [ Images ] for 11, again off Watson, and the prospect of bowling England out looked increasingly likely.
Watson bowled Swann for his fourth wicket off the first ball of the last over with England still needing four runs from five deliveries.
The second and final match of the series takes place at the Melbourne [ Images ] Cricket Ground on Friday.