Duminy clubbed two boundaries off van der Merwe and a six over long on off Vinay Kumar.
With 10 needed from the final over, Robin Uthappa (47) hit two boundaries.
But Sri Lanka soon restored order as Mahela Jayawardene cut and pulled Shoaib for two boundaries in the same over.
He stayed to carve Thissara Perera over the off-side for two boundaries, before being bowled round his legs by the same bowler.
When Rikki Clarke hit two boundaries from the penultimate over, that left the visitors needing just eight to win from the final over.
Mashrafe Mortaza hit two boundaries in his nine before he became Muralitharan's third victim, trapped lbw after being deceived by a slower one.
Dilshan maintained the momentum and fired two boundaries off former Zimbabwe captain Prosper Utseya in the eighth over to bring the 50 up for his side.
As Australia began their run chase, Plunkett began nervously, with two wides in his first over and two boundaries conceded to Adam Gilchrist in his second.
BBC: SPORT | Cricket | England | England seal historic one-day win
Scotland's most-capped player Wright struck two boundaries off Agarkar but the seamer claimed his second wicket with a slower one that Hamilton missed as he tried to sweep.
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And a slight panic set in when Azhar Mahmood edged John Wood behind for 15, and Tudor was lbw to Gary Keedy having hit two boundaries from three deliveries.
Kallis hit only two boundaries in making his 69th one-day fifty before he was dismissed in the 34th over, while several players struck cameos without going on to a significant score.
After Morne Morkel and Wayne Parnell had plundered two boundaries apiece to take South Africa within a whisker of 300, Zaheer Khan wrapped things up in his opening over, trapping Parnell with a clear lbw.
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With five overs to go, 42 were still needed with six wickets in hand, but Kevin O'Brien deposited Mortaza into the stands and two boundaries off the next over, from Rubel Hossain, relieved all the pressure.
With the scoreboard reading a healthy 134-1, Masakadza had already hit two boundaries in Thilan Thushara's last over when he tried another lusty strike from the final ball of the over, with 38 needed off 37 balls.
He hit successive deliveries from off-spinner Harbhajan Singh for four and six and shortly after took an even heavier toll of left-armer Pragyan Ojha with two boundaries followed by another six over mid-wicket to take him into the 90s.
Cameron White fell cheaply and David Hussey, Brad Haddin, James Hopes and Ryan Harris - making his ODI debut in place of Shaun Tait - hit just two boundaries between them as they got bogged down in the final overs.
But the England man did hit two welcome boundaries to keep his team on course for their win.
He put on 242 with Amla, who stroked two fewer boundaries in an innings spanning 241 balls in Colombo.
When the left-hander took two further boundaries off the first over of spin, bowled by Mahmudullah, Ireland were in great shape.
The scoring was kicked off in the afternoon when Cook muscled Hauritz through midwicket for two more boundaries to go to 75.
Although Matt Prior hit two stylish boundaries he was hopelessly deceived by Johnson's slower ball, through his drive early and easily caught at cover.
Jaffer took two more boundaries off Sidebottom to move to 22 before skying an attempted hook against Tremlett to gully, where Kevin Pietersen claimed the catch.
He picked up two quick boundaries, both off Kallis, but then attempted something a bit too inventive off the same bowler - trying to play a ball outside off-stump through the on-side.
Broad passed his previous highest of 42 with two classical boundaries reminiscent of his father Chris in his pomp during the 1986-87 Ashes, a back foot punch followed by a dreamy cover drive.
Ashraful struck two more boundaries in the next over but acting captain Johan Botha brought himself into the attack to bowl the sixth over and clean bowled his counterpart with his first delivery.
The gentle medium pace of Jesse Ryder, who was called on to bowl the fifth over, could not staunch the flow: Coetzer drilled a wonderful six over wide mid-off either side of two further boundaries.
It was left to player of the match Shaw (17 not out) and Holly Colvin to steer the team over the finishing line, with the former hitting two timely boundaries to ease the tension when the pressure had seemed to be getting to England.
The impervious Kallis produced a typically chanceless innings, consuming 290 deliveries featuring 13 boundaries and two sixes, while Amla provided more than adequate support, adding 11 boundaries on the way to his eighth Test match hundred.
He smashed 16 boundaries and two sixes before running out of partners, having shared a ninth-wicket stand of 82 with Steffan Jones, on 113.
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