Dawid Malan bludgeoned 140 before Reece Topley destroyed the Bangladesh top order on Tuesday as England bounced back from their mauling by New Zealand in their Cricket World Cup opener.
In-form Malan belted five sixes in his career-best one-day international score and Topley took 4-43 as the defending champions won by 137 runs after piling up 364-9 in Dharamsala.
England failed to make the most of an ominous position of 296-2 in the 40th over due to some disciplined bowling by paceman Shoriful Islam and off-spinner Mahedi Hasan, who took seven wickets between them, but ultimately had enough on the board.
England captain Jos Buttler was delighted his team had bounced back strongly after their nine-wicket defeat by the Black Caps.
"We stuck to our guns, played in the fashion we want to play and still feel like there's always areas we can improve as well," he said.
"At the back end of the innings we would have liked to maybe have got a few more... but the opening partnership from (Jonny) Bairstow and Malan was brilliant and then Malan and (Joe) Root, fantastic."
Bangladesh were reduced to 14-2 in the second over of their reply, with Tanzid Hasan and Najmul Hossain Shanto unable to cope with the pace and movement of the towering Topley, who replaced Moeen Ali in the side.
That became 26-3 when captain Shakib Al Hasan was bowled by the paceman and the expensive Woakes then got in on the act, enticing an edge from Mehidy Hasan Miraz, with Buttler taking the catch behind the stumps.
Liton Das looked untroubled at the other end, reaching his fifty off 38 balls but his fine innings came to an end in the 21st over when he edged a slower ball from Woakes behind to Buttler and departed for 76.
Topley celebrated his fourth wicket when Mushfiqur Rahim (51) slashed him to deep third man, into the safe hands of Adil Rashid.
As the run rate climbed the result looked increasingly inevitable and the game ceased to be a meaningful contest.
Earlier Malan, who has displaced Jason Roy at the top of the order, hit his fourth ODI century in 2023 in an impressive show of timing and power at the picturesque Himalayan ground.
His opening partner, Bairstow, reached a half-century in his 100th ODI but was bowled by Shakib for 52 to leave England 115-1 in the 18th over.
Former Test captain Root picked up where Bairstow left off, signalling his intent with a ramp shot for six.
Player-of-the-match Malan, 36, reached a stylish century in 91 balls before cutting loose in devastating fashion, smashing 20 runs off just four balls during a Mehidy over.
Bangladesh, who beat Afghanistan in their opening match in India, finally got the breakthrough they desperately needed when Mahedi bowled Malan.
Buttler, with Ben Stokes still out injured, promoted himself up the order and briefly flickered before departing for 20 off 10 balls.
Root, who is now England's all-time top-scorer at World Cups, overtaking Graham Gooch, holed out for 82, top-edging a Shoriful ball that was caught by wicketkeeper Mushfiqur.
Wickets kept tumbling — Shoriful finished with figures of 3-75 and Mahedi took 4-71 — but the total proved well beyond Bangladesh.
"I thought that we didn't start well enough, the first 10 overs especially, and when you give them a sniff, the quality they have in that dressing room, they will always come hard at us," said Shakib.
"We came back strongly in the last 10 overs but it was too late and when you lose four early wickets in 10 overs you are not going to chase 350."
The 10 teams at the World Cup play every other side once in a single round-robin format, with the top four teams progressing to the semi-finals.