Three wickets fell in the final over as Mady Villiers looked to have done enough to turn the game back in England's favour, only for Dalzell to take full advantage of a misfield from Hollie Armitage and win it off the final delivery.
The match had been reduced to 22 overs per side after four-and-a-half hours were lost to rain, and England were then bowled out for 153 - despite 52 off 42 balls from Tammy Beaumont - as Ireland's Aimee Maguire claimed 5-19.
STUNNING WIN 🤯— ICC (@ICC) Ireland hit a boundary off the final ball to script a historic victory 🤩#IREvENG �: https://t.co/IYFGM9FuoT pic.twitter.com/FcYH7DZd1gSeptember 11, 2024
Gaby Lewis led the Irish charge as they chased down their target, but the game first swung back in England's favour in the 19th over when she edged behind off Lauren Filer to fall for 72 from 56 deliveries.
That was the first of two wickets in the over as the hosts slipped to 4-138 for and England found some late momentum.
The game remained on a knife-edge as Ireland continued to edge towards their target, but they started the final over needing eight.
After Rebecca Stokell took a single off Villiers' first ball, Una Raymond-Hoey scored two off the next, only to be run out from the following delivery.
Villiers then bowled both Alice Tector and Jane Maguire for ducks as England sensed victory, only for Dalzell to come in and hit the lone delivery she faced to the ropes, with Armitage running past the ball, perhaps hampered by the low sun late in the day.
England had already taken victory in the three-match series, but this was beyond a mere consolation win for Ireland after a more than two-decade wait.
"Ireland fully deserved their win and deserve a lot of credit for the way they played," England captain Kate Cross said.
"I am proud of the way the team stuck at it. Overall, we've earned a series win and qualified for next year's ICC Women's Cricket World Cup so we've achieved what we set out to do.
"There are areas of the game we can improve on. There are a number of factors which contributed to the result but we still got really close so there are good things to take from it as well."
