England came out in a hurry and Phil Salt hit the first two balls for sixes before being bowled with the third, Bilal Khan's delivery deflecting off the inside edge of the bat and onto the wicket.
Will Jacks then went for five, caught by Kashyap Prajapati off Kaleemullah and England were 20-2 after two overs before Jos Buttler (24 not out off eight balls) and Jonny Bairstow (eight not out off two) got the job done in 3.1 overs.
"I thought the tone was set really well by the bowlers, picking up the early wickets," said captain Buttler, who smashed four fours and a six in the third over.
Bairstow then hit a final four to end the match.
"Job done today, another big game in two days' time," said Buttler.
England play Namibia on Saturday while Australia play Scotland the same day.
A win for England and defeat for Scotland will send the holders through along with already-qualified Australia, who bowled Namibia out for 72 on Tuesday.
England's Group B opener against Scotland in Barbados was washed out and a loss to Australia meant they had to win their remaining two matches to move level on points with the Scots, who had a significantly superior net run-rate.
Australia have six points to Scotland's five and England on three after three matches each.
"We had a point to prove after the last couple of games," said Wood.
Published 14 June 2024, 00:47 IST