Captain Stirling moved on to a career total of 10,017 runs across Tests, ODIs and T20 internationals with a knock of 54 off 64 balls before being caught by Gudakesh Motie off the bowling of Roston Chase in Wednesday's clash.
Building on the first-wicket partnership of 109, fellow opener Balbirnie went on to make 112 from 138 deliveries, including nine fours and four sixes, while Harry Tector chipped in with 56 as the hosts closed on 6-303 after being put in to bat.
West Indies pace bowler Alzarri Joseph claimed the wickets of Balbirnie and Tector before Matthew Forde registered 3-68 by removing ODI debutant Cade Carmichael (16), Lorcan Tucker (30) and George Dockrell (one).
Ireland's attack made light work of the tourists' top order to pave the way for a commanding success as Barry McCarthy and Dockrell starred with the ball.
After opener Evin Lewis was run out by Tector, McCarthy took three wickets and seamer Thomas Mayes marked his ODI debut by clean bowling visiting captain Shai Hope for two to reduce the Windies to 5-31 inside 10 overs.
Justin Greaves offered some resistance with a knock of 35, which was halted by Josh Little, before Dockrell claimed the crucial wicket of Chase for 55 and then dismissed Joseph for a duck and Motie for eight for figures of 3-21.
McCarthy finished with 4-32 after having Forde caught by Little for 38 at the start of the 35th over as Ireland wrapped up victory with 95 balls to spare.
The three-match series continues on Friday before concluding on Sunday.
