Stirling, at his seventh World Cup, shared in a blistering 73-run opening stand with captain Andy Balbirnie to supercharge Ireland’s run chase.
The final Super 12 slot will be decided later Friday when Zimbabwe meet Scotland.
The West Indies won the tournament in 2012 and 2016, but came to Australia with a new-look team after the likes of Chris Gayle, Dwayne Bravo and Kieron Pollard retired, and Andre Russell was overlooked.
They stumbled badly in their opening match against Scotland, crashing by 42 runs, before recovering to emphatically beat Zimbabwe.
But in Ireland, who are playing in their seventh straight World Cup and had only been beyond the first round once before, in 2009, they again hit the wall.
After the West Indies won the toss and batted at a breezy Bellerive Oval in Hobart, the Irish bowlers sent down nine dot balls among their first 15.
In frustration, Kyle Mayers launched at a delivery from Barry McCarthy and was caught by Harry Tector at mid-off for one.
The dangerous Johnson Charles slammed 4-4-6 off Curtis Campher but his luck ran out in the next over, slicing to Campher off spinner Simi Singh for 24.
Brandon King, who missed the West Indies’ last game with illness, was dropped two balls later and made the most of the opportunity, crunching four boundaries to steer them to 67-2 at halfway.
Evin Lewis received treatment for a hamstring issue and was out soon after for 13, ending a 44-run partnership.
Skipper Nicholas Pooran (13) and Rovman Powell (six) didn’t last against a quality attack as King (62 not out) did his best to push the scoreboard forward.
In reply, Ireland got off to a cracking start with Stirling and Balbirnie on a mission, blazing 54 off the first five overs, with eight boundaries, four of them sixes.
The spin of Akeal Hosein finally gave the West Indies a breakthrough in the eighth over with Balbirnie caught by Mayers after an entertaining 37 off 23 balls to end a decisive opening stand.
The run rate dipped but Stirling, in his 177th international, kept going and reached his 21st T20 half-century with another boundary and with Lorcan Tucker (45 not out) saw them home.