Labuschagne departs as Australia lose five against England
Five-time winners Australia slipped to 190-5 in 35 overs after being invited to bat at the world's biggest cricket stadium in Ahmedabad.
Woakes removed both openers to leave Australia on 38-2 before Steve Smith and Marnus Labuschagne attempted to steady the innings in a partnership of 75.
Leg-spinner Rashid broke the stand with Smith out on 44 and then had Josh Inglis (three) caught at backward point after the batsman attempted a reverse sweep.
Labuschagne reched his 50 and put on a partnership of 61 with Cameron Green before falling to Mark Wood. He made 71.
A win will boost Australia's chances of a semi-final berth as they stand third in the 10-team table led by hosts India, who have already made the final-four.
England are all but out of the race for the semi-final with five losses in six matches and another defeat will officially end their campaign.
A win, however, will be a boost to their hopes of qualifying for the 2025 Champions Trophy with the top seven teams from this World Cup gaining entry into the tournament where hosts Pakistan will have automatic qualification.
Fast bowler Woakes struck in his first over to send back previous-match centurion Travis Head, caught for 11 after the left-hand batsman edged an angled delivery to Joe Root at slip.
David Warner attempted to hit back with a four and a straight six off Woakes before the bowler had his revenge when the left-hander mishit a slower off-cutter and was caught.