Chasing 285 to win, after opener Rahmanullah Gurbaz had hit a blistering 80, England were bowled out for 215 despite Harry Brook's 66 with spinners Mujeeb Ur Rahman and Rashid Khan claiming three wickets each.
The stunning upset gave Afghanistan just their second World Cup win to add to a lone victory over Scotland at the 2015 tournament.
They came into Sunday's clash having lost their opening two games in India and on a 14-match losing World Cup streak.
"Very proud moment to be here in the World Cup and beating the champions, it's a great achievement for the whole region. I'm so happy with this performance," Mujeeb said.
"As spinners, it's hard to bowl in the powerplay, but I've been working in the nets to be as consistent as possible... We knew dew would be a factor."
After Gurbaz and the recalled Ikram Alikhil, with 58, had given them a decent target to defend, Afghanistan's bowlers went to work, striking at regular intervals.
Jonny Bairstow (two) was lbw to Fazalhaq Farooqi in the second over before Joe Root was clean bowled by 22-year-old man of the match Mujeeb for 11.
Mohammad Nabi got rid of Dawid Malan, who made 140 against Bangladesh, for 32 to precipitate a slide which saw England slump to 138-6.
Skipper Jos Buttler was clean bowled by seamer Naveen-ul-Haq for nine, Rashid Khan had Liam Livingstone lbw on 10 before Nabi also dismissed Sam Curran (10).
England were tied down, at one stage going more than eight overs without hitting a boundary until Brook managed the team's lone six of the innings in the 31st over.
Mujeeb sent back Chris Woakes before effectively sealing the game in his next over, having Brook caught behind by Alikhil with England at 169-8.
Brook's 66 came off 61 balls with seven fours and a six.
Late fireworks from Adil Rashid (20), Reece Topley (15) and Mark Wood (18) only served to take England past the 200 mark.
Earlier, Gurbaz piled up his runs off 57 balls with eight fours and four sixes to register his eighth score in excess of fifty in his ODI career.
However, he was furious that he was unable to go on to make a sixth century when he was involved in a disastrous run-out mix-up with captain Hashmatullah Shahidi in the 19th over.
Gurbaz failed to make his ground and Buttler whipped off the bails from a throw by substitute fielder David Willey.
Gurbaz run-out anger
An angry Gurbaz smashed his bat into a chair as he departed with his team on 122-3.
Gurbaz had needed just 33 balls to get to his half-century as Afghanistan, put into bat, stormed to 100 without loss from 77 deliveries.
Once Gurbaz was dismissed, England's spinners dragged the champions back into the contest in the middle overs.
The impressive Adil Rashid finished with 3-42 from his 10 overs having initially broken Afghanistan's 114-run opening stand when he had Ibrahim Zadran (28) caught.
But Alikhil chimed in with a 66-ball 58 after surviving being hit on the shoulder by a 147 km/h delivery from fast bowler Mark Wood.
Mujeeb added 28 to the total off 16 balls as Afghanistan finished strongly.
England's seamers endured a day to forget with Sam Curran conceding 46 runs off four overs and new ball bowler Chris Woakes coughing up 41 off his four.
"Disappointing, a tough loss to take. Congratulations to Afghanistan, they outplayed us today. We were not at the level we wanted to be with the ball and the bat," Buttler said.
"Afghanistan have a really skilful attack... They put us under a lot of pressure."
England are fifth in the group standings with one win from three matches, one place ahead of Afghanistan.
