Balbirnie plundered 77 from 55 balls, including 10 fours and two sixes, and his partnership of 76 with Harry Tector (36) edged Ireland closer to victory.
Curtis Campher (15*) and Gareth Delany (10*) saw them over the line to secure the win with one ball to spare.
Despite an early setback, Pakistan started strong, with Babar Azam hitting 57 and Saim Ayub adding 45.
However, Craig Young’s strong performance saw him take 2-27 as Ireland took control to limit the visitors in the later stages as Azam Khan and Shadab Khan both walked without getting any runs.
The sides will meet again at the Dublin venue on Sunday and Tuesday.
Data Debrief:
Ireland achieved their target of 183 against Pakistan successfully today, making it their highest run chase against a full-member side in men's T20Is.
Ireland's first win against Pakistan came at the 2007 World Cup and 17 years later they secured a first victory over them in T20 cricket.
St Kitts & Nevis Patriots won the toss and chose to field first, with the Royals getting off to a subdued start, reaching 55-2 after 10 overs before a superb 102-run partnership between Azam Khan and Harry Tector propelled them to 156-3 after 20 overs. In their chase, the Patriots got off to a confident start with Andre Fletcher and Evin Lewis building a platform but faltered as the wickets tumbled in the final five overs to leave them 120 all out after 20 overs, losing by 36 runs.
Barbados Royals, who have already secured a place in next week’s playoffs, got off to a very cautious start in their innings, losing openers Rahkeem Cornwall and captain Kyle Mayers in the first eight overs. Sheldon Cottrell, returning to the Patriots' side, led by example in the early overs with a disciplined performance. Yet Khan and Tector revived the Royals innings with some fantastic shot-making that helped reap 95 runs in the final eight overs to take the Royals to 156-3.
St Kitts & Nevis Patriots had got off to a positive start, Fletcher and Lewis navigating their way through the PowerPlay, before Mujeeb ur Rahman took both wickets. The Patriots never found consistency after that, losing seven wickets in the final five overs of the game, as Mujeeb found support from Nyeem Young, who also took three wickets.
The win means Barbados Royals continue their excellent form this season while the Patriots are outside the play-off spots with one game left to play.
Scores: Barbados Royals 156-3 (Khan 64, Tector 47*; Dananjaya 1-25, Jansen 1-32) beat St Kitts and Nevis Patriots 120 all out (Lewis 41, Brevis 21; Young 3-5, Mujeeb 3-18) by 36 runs.
