Chasing a revised 122, Tigers skipper Mohammad Ashraful hit 21 off 10 balls but three wickets fell in six balls.
But Mohammad Ashraful made 64 and captain Shakib Al Hasan 65 as the tourists reached their target with six balls to spare.
But Dave Langford-Smith and Thinus Fourie (14 not out from six balls) scrambled 22 from the final 12 balls to set Scotland their daunting target.
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Skipper Paul Collingwood was delighted with Pietersen's form and the way he chased down the target of 136-5 to help England home with six balls to spare at Trent Bridge.
Despite Key's best efforts, three wickets fell for just one run in six balls, Andre Nel trapping Matt Prior for one, and adding the wicket of Samit Patel for a golden duck.
They needed 15 to win from the final six balls but fell short, with Ali unbeaten on 31 alongside Syed Tariq Hussain, one not out, as the Scots held on for victory.
Inevitably, Bopara sold Cook horribly short when pushing to cover and setting off for a mad run - Cook was run out by yards - and Graeme Swann lasted just six balls.
Alam swiped his third ball over the VIP stand at mid-wicket and when he just cleared long-on for six more in the next over from Fernando it left 13 needed from the final six balls.
Starting the match ranked the best batsman in Test cricket, the veteran left-hander lasted a total of six balls across both his innings - here squeezing a catch off bat and pad to silly point.
Trott lasted only six balls, dragging an innocuous delivery from Johnson into his stumps, and with 98-0 suddenly becoming 99-2 there were fears that the match might be following a similar course to the Perth Test.
The biggest plus for Bangladesh was the bowling of Robiul Islam, who looked to be the first Bangladeshi quick to be able to put six balls in the same place since Mashrafe Mortaza's brief, injury-curtailed ascendancy.
When he thrashed left-arm seamer Parnell through the covers for four and upper-cut him for six two balls later the dashing Indian opener had made 39 from 20 balls.
BBC: India lead South Africa with huge stand in Kolkata Test
Because you can bowl six legitimately good balls in the limited-overs game and they can disappear to six different parts of the ground.
Fraser Watts made a scratchy six from 28 balls before he edged RP Singh to give keeper Mahendra Dhoni a simple catch off the final ball of the eighth over.
And despite a few nervous moments, it was left to Malik to seal victory, smashing the ball for six with three balls to go before sparking scenes of celebrations amongst his teammates.
The 25-year-old Warren, who holed the winning putt in the 2001 Walker Cup, spent six hours hitting balls with coach Bob Torrance on Monday, and it paid instant dividends with a bogey-free round.
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The partnership was the highest for Yorkshire's ninth wicket against Hampshire, and the highlight was Bresnan blasting Shane Warne for four and six in consecutive balls en route to his Championship best of 79.
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Off-spinner Graeme Swann did not enter proceedings until midway through the afternoon session and his first over was a forgettable one as Haddin helped himself to a four and a six off successive balls.
He needed six from two balls to set the fastest fifty in Test cricket - a record many would be surprised to learn is held by South Africa's Jacques Kallis - but was briefly becalmed.
BBC: India lead South Africa with huge stand in Kolkata Test
But he was unable to achieve a breakthrough and Sehwag, who hit a four and a six off successive balls in Makaya Ntini's opening over, pushed Steyn through the covers to reach a 59-ball half century in the final over of play.
Johann Louw, batting at number nine, hit the first two balls he faced for six and raced to 23 off seven balls.
Player of the tournament Claire Taylor hit an unbeaten 39 as England won by six wickets with 18 balls to go.
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In a low-quality, low-scoring affair at Trent Bridge, Bangladesh struggled to 137-8, and Ireland got home with six wickets and 10 balls to spare.
Ponting will perhaps never have made a scratchier six, from 21 balls, and was lbw after losing his balance trying to play across his pad.
But when Patel mis-timed a drive at Robin Martin-Jenkins' first ball it began an astonishing collapse which saw six wickets fall for six runs in 24 balls.
Ramdin, playing in just his fourth Test, bettered his previous top score of 56 with a controlled display, hitting six boundaries off 190 balls before nicking a catch off MacGill to Warne at slip.
Then, the following day, Pune went a step further: Requiring 19 from 19 balls with six wickets in hand at home to Hyderabad, the team managed just seven of them before it was bowled out.
He chipped a simple return catch to Rashid in the 10th over with 60 needed, but even after his departure the Irish were in prime position with 42 needed from 54 balls and six wickets in hand.
Fellow opener Alex Obanda delighted a healthy crowd by smashing Tait back over his head for a massive six, but three balls later the paceman got his revenge as a low full toss demolished Obanda's middle stump.
By way of comparison, Michael Yardy, although impressive in the series against Australia averaging over eight in the powerplay, has only hit one six from 455 ODI balls faced and has a strike rate barely above 70 - yet is a regular feature in the overs when aggressive hitting can have devastating effect.
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