Bangladesh make history to dash Pakistan's World Cup hopes
Pakistan appeared to be cruising to victory, powered by a maiden century for Sidra Ameen, but slumped to a nine-run defeat after losing six wickets for 26 runs.
It was Pakistan's fourth straight loss at the tournament in New Zealand and gives them virtually no chance of making the playoffs.
"It's very hard to digest, we were in the game but some poor shots from the middle order cost us the game," captain Bismah Maroof said in Hamilton.
Bangladesh skipper Nigar Sultana praised her side's never-say-die approach.
"I cannot describe this in words because it's our first ever win in a World Cup and this is history that we've made today here," she said.
"We're looking forward to carrying this momentum through the tournament."
Pakistan won the toss and opted to bowl but the strategy backfired after Fargana Hoque inspired Bangladesh to 234-7, their highest one-day international total.
Hoque made 71, forging a 96-run partnership with Sultana, who finished on 46, while Sharmin Akhter contributed a well-hit 44.
Nashra Sandhu was the pick of the Pakistan bowlers with 3-41, including two wickets in successive balls, one of which dismissed the dangerous Hoque.
Pakistan openers Ameen and Nahida Khan set about chasing the 235-run target with gusto, producing a 91-run partnership which ended when Khan was bowled by Rumana Ahmed.
Ameen ploughed on and seemingly had Pakistan on the brink of victory at 183-2 in the 42nd over, needing 52 runs from 48 balls with eight wickets in hand.
But disaster struck as the batters threw away their wickets, with three departing for first-ball ducks as spinner Fahima Khatun produced a mesmerising spell on her tournament debut to claim 3-38.
Any glimmer of hope for a Pakistan win ended when Ameen was run out for 104 in the 48th over.