Making his first England appearance in over a year, paceman Archer dismissed Azam Khan and Imad Wasim as Pakistan were bowled out for 160 while chasing 184.
England captain Jos Buttler was the star of the show in Birmingham, plundering 84 off 54 balls to set the tone for the hosts' innings.
Will Jacks chipped in with a useful 37 before he, like Buttler, was caught out by Shadab Khan from Haris Rauf's bowling.
Shaheen Shah Afridi (3-36) stopped Jonny Bairstow, Moeen Ali or Chris Jordan from getting going, but Archer came in to hit a four and a six to get England to 183-7.
Pakistan were two down within four overs of their chase, and after Babar Azam (32) and Fakhar Zaman (45) were dismissed by Moeen and Liam Livingstone respectively, their chances looked increasingly slim.
Having taken out Azam, Archer (2-28) ended Wasim's stand at 22, with Reece Topley (3-41) and Jordan (1-31) finishing the job for England.
The series now moves to Cardiff, with the final match taking place at The Oval on Thursday.
Data Debrief: Buttler at his best
Buttler may well have to miss part of the upcoming T20 World Cup due to the birth of his third child, and England will be hoping their skipper makes a swift return to action if that is indeed the case.
His knock, which included eight fours and three sixes, marked the second-highest score by an England captain in a T20I, behind Eoin Morgan's 91 against New Zealand in 2019.
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.
The Black Caps took an unassailable 2-1 lead in the five-match T20I series, thanks in the main to Tim Robinson (51) and bowling duo William O'Rourke (3-27) and Ben Sears (2-27) on Thursday.
Set a target of 179 to win, Pakistan looked on their way to victory when Fakhar Zaman got going, but he was eventually dismissed on 61 by Sears.
Abbas took three wickets in New Zealand's innings, yet he could only contribute a single run to Pakistan's cause as the hosts fell just short in Lahore.
Data Debrief
Shadab Khan did not bowl a single delivery for Pakistan, which is the first time that has happened in a completed T20I innings.
He did take an exceptional catch to dismiss Mark Chapman, but it was not enough to inspire Pakistan.
Pakistan, after winning the toss and batting first, posted a score of 269-9 off their 50 overs thanks to a top score of 86 off 78 balls from all-rounder Shadab Khan. His knock included four fours and three sixes.
Opener Imam-ul-Haq provided support with a 68-ball 62, his seventh consecutive score of at least 50 in ODIs.
West Indies Captain Nicholas Pooran, usually a wicket-keeper, was the star of the show with the ball taking 4-48 off his 10 overs. Returning all-rounder Keemo Paul took 57 off nine overs.
Akeal Hosein then top-scored for the tourists with a brilliant 60 off 37 balls including two fours and six sixes but it wasn’t enough as the Windies ended up being bowled out for 216 in just 37.2 overs.
Keacy Carty (33) and Shai Hope (21) also made meaningful contributions with the bat against 4-62 from Shadab Khan and two wickets apiece from Mohammad Nawaz and Hasan Ali.
Khan was voted man of the match while ul-Haq took home man of the series.
The Falcons, who opened their campaign with a win on Monday, put the Strikers in to bat after winning the toss.
Colombo made use of the opportunity, posting 198-7 from their 20 overs.
It was a collective effort with the bat for the Stars as Sadeera Samarawickrama, skipper Thisara Perera, Muhammad Waseem, Chamika Karunaratne and Shadab Khan all made solid contributions.
Samarawickrama led the way with 48 from 26 balls including seven fours and a six while being well supported by Perera (38 off 30), Waseem (32 off 18), Karunaratne (25* off 10) and Khan (20 off 17).
Falcons captain Wanindu Hasaranga took 2-30 from his four overs.
The Falcons got starts from Dinesh Chandimal, Hasaranga, Angelo Mathews and Andre Fletcher but they weren’t enough as their chase fizzled out, eventually being dismissed for 147 with one ball left in the 16th over.
Chandimal made a top score of 38 while Hasaranga, Matthews and Fletcher made scores of 25, 25 and 24, respectively.
Shadab Khan led the way with 4-22 from his four overs including the tournament’s first hat-trick in the 15th over.
Action continues on Wednesday when the Dambulla Sixers take on the Jaffna Kings at 4:30 AM before the Colombo Strikers face the Galle Marvels at 9:30 AM (Jamaica Time).
It was a nervy start by Pakistan, who lost two wickets in the first three overs, but captain Babar Azam eventually finished as their top scorer, limping to 44 after a slow power play.
However, the US bowled well, with Nosthush Kenjige proving a particular thorn in their side as he finished with 3-30. Pakistan ended on 159-7, with the help of Shadab Khan's 40.
Monank Patel brought up his 50 off 38 balls at the end of the 13th over before being caught by Rizwan, with the home fans starting to believe they could be watching a major upset.
Though two wickets in seven balls slightly dented the mood, the US finished the second innings strongly, with Aaron Jones plundering 36, including two boundaries, before Nitish Kumar struck a four on the final ball to keep the game alive.
Jones and Harmeet Singh caused more problems in the super over, impressing with an 18-0 as Pakistan failed to find any composure.
Ultimately, it was Kumar who proved the hero once more, as he caught out Iftikhar Ahmed as Pakistan failed to chase down the target, and the hosts sit top of Group A after two victories.
Data Debrief: Pakistan stunned
Another pick of the bunch in the US' bowlers was Saurabh Netravalkar, who finished on 2-18, before taking the all-important wicket in the super over. He has now become the top wicket-taker for the US in T20Is with 29, going past Nisarg Patel's 27.
Steven Taylor has also broken the record for the most catches by a fielder (10) in T20Is for the US, going past Patel's nine.
And despite being on the losing side, Amar created some history of his own as he became the top scorer in T20Is with 4067 runs, surpassing Virat Kohli's 4038.
