Opening batsman Salt led the way as England chased down a target of 197 with 14 balls to spare to go 1-0 up in the three-match series.
Jacob Bethell, 21, became England's youngest men's captain in an international match, breaking the record of Monty Bowden, who was aged 23 years and 144 days when he captained England against South Africa in 1889.
The all-rounder is leading England in the series in Ireland in place of rested all-format mainstay Harry Brook.
Salt scored 141 not out, England's highest individual T20 total, in their jaw-dropping score of 304-2 against South Africa at Old Trafford last week.
England fielded a much-changed side in Dublin, but Salt enjoyed another blistering first-wicket partnership with Jos Buttler at Malahide, with the pair racing to 74 inside five overs.
"I enjoyed that," said Salt. "It's a pretty good wicket and a good ground to bat on when you get going. It was fun.
"We both try and take it on fairly early, when it works, it looks good."
Buttler (28) was first to go, but Salt continued his rampage, striking 10 fours and four sixes in 46 balls before he was caught off the bowling of Graham Hume in the 16th over.
Earlier, Bethell fell for 24, holing out tamely to extra cover.
"It feels pretty special," said Bethell. "Winning the first one is always nice."
Ireland posted 196-3, with Harry Tector (61 not out) and Lorcan Tucker (55) providing the bulk of their runs, but that total was soon put into perspective as England took the game by the scruff of the neck.
"We couldn't have asked for much more from our batters," said Ireland captain Paul Stirling.
"To score 196 in the end was great."
The teams will meet again at Malahide on Friday, with the final match of the series taking place two days later.