Balbirnie played all four Afghanistan spinners with ease, and together with George Dockrell (54), shared a match-winning, 143-run stand for the fifth wicket, after Ireland was in trouble at 73-4 in the 16th over.
Earlier, Najibullah Zadran smashed 104 off 98 balls and his maiden ODI hundred for Afghanistan. Captain Asghar Afghan (75) shared a century stand with Zadran, after Ireland reduced Afghanistan to 74-5 in 19 overs.
The fourth match will be on Friday.
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