Afghanistan became the first team to be eliminated after an agonising 11-run loss against India on Saturday.
Southampton: Bangladesh's Shakib Al Hasan became the leading run scorer in this year's World Cup so far as he made a confident start in Monday's match against minnows Afghanistan.
Shakib's unbeaten 31 took him to 456 runs in the tournament, while Mushfiqur Rahim was six not out in Bangladesh's 95-2 after 20 overs in Southampton.
Afghanistan captain Gulbadin Naib won the toss and elected to bowl first after the start of play was delayed 10 minutes by light rain.
Liton Das was promoted ahead of Soumya Sarkar to open along with Tamim Iqbal for Bangladesh, with the pair managing a brisk 23 from the first four overs.
But Das fell for 16 in the next over after being fooled into a miscued drive by Mujeeb Ur Rahman.
Hashmatullah Shahidi dived forward to get his fingers underneath the ball at extra cover, with a review confirming the dismissal.
That brought Shakib to the crease and he upped the tempo even further with some aggressive hitting that maintained his fine World Cup form.
When Shakib, who has two centuries already in the tournament, pulled Naib to the boundary, it moved him above Australia's David Warner's 447 runs as the leading scorer in this year's event.
Tamim and Shakib put on their fourth successive fifty partnership in one-day internationals.
But having been hit for a boundary the ball before, Mohammad Nabi responded with flighted turner that bowled Tamim for 36.
Shakib survived an lbw review off Afghanistan's star leg-spinner, Rashid Khan, when he had made 27, the ball-tracking review showing it would have gone just over the stumps.
Victory for Bangladesh would move them into fifth place in the 10-team table.
That would leave Bangladesh within one point of fourth-placed England, who play Australia on Tuesday, as the race hots up to qualify for the semi-finals via a top-four finish.
Afghanistan became the first team to be eliminated after an agonising 11-run loss against India on Saturday when Mohammed Shami's final-over hat-trick denied them a famous upset.