Set a target of 329 — the same score they finished on to beat England at the 2011 World Cup — the Irish laid the foundations with a 214-run stand between Stirling and captain Balbirnie in the final match of the Royal London series on Tuesday.
Stirling was run out for 142 while Balbirnie holed out for 113 with 50 still required from 33 deliveries, but Kevin O'Brien - the hero of Bangalore - fittingly got them over the line from the penultimate ball with seven wickets to spare under lights.
After being asked to bat first, England had stuttered to 44-3 but Eoin Morgan's 106 from 84 balls was the cornerstone of 328 all out in 49.5 overs, the captain sharing a 146-run stand with Tom Banton.
England won the series 2-1 but Balbirnie took pride in the fact that his team can now boast victories over both white-ball world champions, having toppled the West Indies in Twenty20 in January.
“We've beaten the T20 world champions in their own backyards and we've beaten the ODI champions,” Balbirnie said.
“It's a huge win for us and this group. For the young guys to be involved in this series but to also be involved in a win like that is special and one we'll remember forever.
“I don't know if it's sunk in. Hopefully we've given the kids and the young generation a bit of a boost and something to strive towards.”