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Ireland 183 for 5 (Balbirnie 77, Tector 36, Abbas 2-36) beat Pakistan 182 for 6 (Babar 57, Ayub 45, Young 2-27) by five wickets
A brilliant 77 from opener Andrew Balbirnie helped the hosts to 183-5 to win with just one ball to spare.
Pakistan made 182-6, with Babar Azam hitting 57 and Saim Ayub adding 45.
Ireland's first win against Pakistan came at the 2007 World Cup and 17 years later they secured a first victory over the tourists in T20 cricket.
After losing an early wicket Babar and Ayub put on 85 runs to lay a solid foundation for Pakistan.
But they went from 116-2 to 123-5 before a quickfire 37 from Iftikhar Ahmed saw them post a competitive total.
Craig Young was the best of the Irish bowlers with 2-27.
Ireland were 27-2 before a partnership of 76 between Balbirnie and Harry Tector (36) put them on course for victory.
George Dockrell's 24 saw the Irish edge closer and when Balbirnie was dismissed they needed 17 from eight balls.
Curtis Campher (15*) and Gareth Delany (10*) saw Ireland home, with a leg bye sparking celebrations.
The sides will meet again at the Dublin venue on Sunday and Tuesday.
Ireland and Pakistan will also go up against each other in their concluding World Cup group game in Florida on 16 June.
