Among those dismissed in the spectacular late collapse on Monday was Sidra Ameen, run out for 104 after posting the first century by a Pakistan batter at a Women's World Cup.
Pakistan were 2-183 after 42 overs in Hamilton, seemingly well placed to surpass Bangladesh's total of 7-234 with Ameen in command.
But legspinner Fahima Khatun, playing her first match at the tournament, sparked the collapse with three wickets and two run-outs added to the chaotic ending.
Player of the match Khatun (3-38) claimed the wicket of Omaima Sohail (10) before removing trapping Aliya Riaz and Fatima Sana, both for first-ball ducks.
Pakistan lost those five wickets in the space of two overs and endured their most bitter blow when Ameen was run out after doing so much to steer her team toward a first win of the tournament.
"It's a hard loss to digest," Pakistan captain Bismah Maroof said.
"Sidra (Ameen) will be disappointed. She was playing really well and will be disappointed she didn't finish the game.
"We were in the game, we should have chased it down but the poor shot selection cost us."
Pakistan won the toss and followed the overwhelming trend of the tournament in which most teams have chosen to chase.
A 96-run partnership for the third wicket between Fargana Hoque (71 from 115 balls) and Nigar Sultana (46 from 64) set up Bangladesh's innings while opener Sharmin Akhter made 44 from 55.
Nashra Sandhu (3-41) was the pick of Pakistan's bowlers.
"I can't describe this in words because this is our first-ever win in a World Cup and this is history we've made today," Bangladesh captain Sultana said.
"Now we're looking to carry this win through the tournament."
Bangladesh have one win from three starts in New Zealand while Pakistan slipped to last place in the eight-team group stage with no wins from four matches.
