The visitors eased to their victory target of 179 with 18 balls remaining as a second-wicket partnership of 139 between Rizwan and Babar proved decisive.
Rizwan’s 56 from 38 balls was his 28th T20 fifty on the international stage, while skipper Babar smashed five sixes – including four from a Ben White over – and six fours in his 42-ball 75.
The key moment came when Babar was dropped on 19 by George Dockrell on the cover boundary off the bowling of White.
Babar punished that mistake in style with some extraordinary hitting, and Pakistan got across the line despite Mark Adair finishing with three wickets.
Ireland’s total of 178 for seven was built around a second-wicket partnership of 85 from 49 balls between Andy Balbirnie and Lorcan Tucker.
Balbirnie struck 35 from 26 balls while Tucker – captain for the first time in the absence of the rested Paul Stirling – made it back-to-back half-centuries after making 51 in the previous game.
Tucker hit 13 fours and a six in a 41-ball 73, but Ireland failed to take full advantage of being 95 for one at the halfway stage.
Shaheen Shah Afridi produced a superb spell of three for 14 from four overs, removing Ross Adair, Neil Rock and Mark Adair.
Harry Tector (30 not out) and Graham Hume (10no) produced late defiance, but the target proved well within Pakistan’s compass for a 2-1 series victory.