England's Topley destroys Bangladesh after Malan's World Cup ton
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.
The total could have been even higher but England subsided from 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.
Bangladesh shot out of the blocks, with Liton Das hitting three consecutive fours off the first over bowled by Chris Woakes.
But they were quickly reduced to 14-2, 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 England captain Jos Buttler taking the catch behind the stumps.
Despite the carnage, Liton looked untroubled at the other end, reaching his fifty off 38 balls as Bangladesh tried to rebuild.
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 Mushfiquir 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, petering out despite some late hitting.
Malan stars
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, Jonny 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 Joe Root picked up where Bairstow left off, signalling his intent with a ramp shot for six.
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.
Then Liam Livingstone had his off-stump flattened first ball as England lost momentum.
Wickets kept tumbling - Shoriful finished with figures of 3-75 and Mahedi took 4-71 - but the total proved well beyond Bangladesh.
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.
