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.
India captain Rohit retired hurt after making 52 in the second innings in New York as Rahul Dravid's side chased a 97-run target with more than seven overs to spare.
The opening batter was struck on the upper arm by a vicious Josh Little delivery in the ninth over, subsequently leaving the field before Rishabh Pant's 36 not out eased India over the line.
Rohit conceded the pain remained in his post-match interview before focusing on the positives of his team's bowling showing, with Hardik Pandya, Jasprit Bumrah and Arshdeep Singh all impressing.
He said: "Just a little sore. New ground, new venue, wanted to see what it's like to play on; I don't think the pitch settled down, there was enough there for the bowlers.
"Stick to your basics, think about Test match bowling. Arshdeep can swing the ball into the right-handers and that set the tone.
"If the conditions are there for the seamers, we wanted them in the squad. The spinners will play their part later in the tournament. We are open to making changes to the team's needs."
Bumrah produced a blistering spell, taking two wickets for just six runs from his three overs as Ireland limped to 96 all out in New York.
"When you come here and the ball is seaming around with some bounce and pace, I would never complain," Bumrah added. "You have to be proactive, you can't preempt things.
"You realise how the wicket is and then go back to what works for you. Once the seam goes down the pitch does settle down.
"You have to be prepared to bowl in all conditions, so very happy today."
India meet fierce rivals Pakistan on Sunday after their opening World Cup victory, and Rohit expects his team to be flexible once again dependent on conditions.
"I don't know what to expect from the pitch but we will prepare as if conditions are going to be like that," Rohit continued.
"That will be a game where all 11 of us need to come together and contribute.
"It was scratchy but good to spend time in the middle, hopefully we can do the same [against Pakistan]."
