Woakes scored 78 to put 196 on board for England in first innings.
Australian captain Steve Smith's decision to bowl paid dividends as England were held to just 196 in the fourth one-day international in Adelaide on Friday.
With the five-match series already in their keeping after winning the first three games, the tourists did well to reach a competitive total following a disastrous start which saw them lose four of their top six batsmen for ducks.
On Australia Day, it was all the home side as the tourists slumped to eight for five in the early overs. Their lowest-ever total of 86 looked in danger until all-rounder Chris Woakes rescued the innings.
It could easily have been six wickets before reaching double figures as well, with captain Eoin Morgan having two near-misses as soon as he came to the crease.
In the end, solid resistance from Woakes (78) along with Morgan and Moeen Ali (33 each) -- and Tom Curran (35) -- enabled England to scramble to a decent total.
Woakes continued his excellent form with the bat in the series, hitting five sixes in the 82 balls he faced before being caught on the boundary off Andrew Tye (3-33).
The rot set in early for England after being sent in by Smith for the second successive match, this time in humid conditions which favoured seam bowlers, as Australia sought to turn around their dreadful recent record of just one win in their past 11 completed matches.
Jason Roy, who got England rolling in the series with a record-breaking 180 in the opening match, fell to the second ball of the innings, caught at point by Smith off the bowling of Hazlewood (3-39) for a duck.
Alex Hales (3) was the second to fall, bowled off his pads by Pat Cummins, who snared a career-best 4-24.
Opener Jonny Bairstow was caught behind from the bowling of Hazlewood for a duck, and Test captain Joe Root also fell without scoring, caught on the fine leg boundary after top-edging a hook shot from the bowling of Cummins.
Jos Buttler, coming off a match-winning century in Sydney, became the fourth batsman dismissed without scoring, caught behind from the bowling of Hazlewood when England had just eight runs on the board.
However, Woakes picked up where he left off in an unbeaten half-century in Sydney and had good support from the previously out-of-form Ali and number 10 Curran.
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