The result drew Pakistan level with Australia, who had already beaten Ireland, on six points. Each team will play one another twice. Australia's first game with Pakistan was abandoned due to the weather.
Chasing a Duckworth Lewis-determined target of 97 in a game reduced to 14 overs a side by rain at Bready Cricket Club, Magheramason, near Derry, the home side managed 6-83.
Having opted to bat after a delayed start, Pakistan lost opener Iram Javed to Ava Canning's first legal delivery, but Muneeba Ali and skipper Bismah Maroof had steered the tourists to 1-32 from six overs when the weather intervened again.
Muneeba fell for 29 and Maroof followed for 13 as Laura Delany made her mark to reduce Pakistan to 3-48 after 9.2 overs and although Ayesha Naseem and Nida Dar put on 40 for the fourth wicket, Dar's departure for 26 saw her side restricted to 5-92.
Delany finished with two for 25 and Jane Maguire two for 14 to give the batters something to work with.
Openers Gaby Lewis and Rebecca Stokell got Ireland's response off to the perfect start as they plundered 25 from the first two overs, but after Stokell was bowled by Tuba Hassan for 19, the momentum was lost.
Needing 18 from the final over, Lewis was run out - one of three dismissals in that fashion - for 47 as three wickets fell in the final five balls.
Ireland meet Australia at the same venue in the next match on Thursday.
