Shamima Sultana was the first batter to fall in the ninth over as she hit Nida Dar straight to midwicket for 17, bringing Fargana to the crease.
The Tigresses finished the powerplay on 51 for one, with Sharmin Akhter on a run-a-ball 29, but some miserly bowling from Pakistan slowed her down before she gloved an Omaima Sohail delivery back onto her own stumps for 44.
That left Bangladesh on 79 for two at the beginning of the 20th over, with Fargana on just eight off 32 deliveries and knowing she now had to step up and anchor the innings. Fortunately for Bangladesh, she did just that.
While miserly Pakistan bowling restricted Bangladesh, Fargana hit a much-needed boundary mid-way through the 25th over as they reached the halfway stage at 92 for two.
Sensing her moment, the No.3 smacked Fatima Sana for successive boundaries at the beginning of the 31st, while she then had an LBW decision overturned after initially being given out.
With Nigar Sultana brilliant at finding ones and twos and Pakistan struggling for wickets, Bangladesh worked their way into a promising position as Fargana brought up her ninth ODI half-century off 89 balls.
Nigar (46) fell in the 40th over after a busy 64-ball innings that brought just one boundary and her replacement, Rumana Ahmed, upped the tempo alongside Fargana.
Successive boundaries helped Bangladesh past 200 in the 44th over but Rumana's 13-ball cameo ended in the next as she holed out off Nashra Sundhu.
The same bowler also removed Fargana two overs later by finding the edge of her bat for 71 and then trapped Fahima Khatun LBW with the very next ball.
Salma Khatun was forced to block the hat-trick ball, while some clever running through the rest of the innings helped Bangladesh to their highest-ever women's ODI score.
Pakistan made a promising start in reply, with Sidra and Nahida Khan at the top of the order. They reached 46 for no loss at the end of the powerplay and then brought up the 50 partnership in the 13th.
The breakthrough came in the 24th over, as Nahida chopped a Rumana delivery onto her own stumps for 43, ending a promising 91-run stand.
Sidra was then dropped twice in the space of three overs, including a simple chance at point from a thick edge, but Pakistan's main concern was an increasing run-rate which had creeped to over six.
They reached the final 10 overs requiring 67 with eight wickets in hand and when they scored 11 off the 41st over, it looked like the game would go down to the wire.
But Sidra was soon running out of partners, as Omaima went for 10 and Nida Dar for a first-ball duck, while the 44th over proved a key turning point.
Fahima Khatun took two wickets in two balls to remove Aliya Riaz and Fatima Sana, before Sidra Nawaz was run out for just one to leave Pakistan on 188 for seven.
Sidra Amin brought up her maiden ODI century shortly after but was run out for 104 in the 48th and though Pakistan needed 16 to win off the last, they fell nine runs short.