Chasing a revised target of 128 from 47 overs in gloomy conditions, Ireland held their nerve to hit the jackpot with 32 balls to spare, when captain Trent Johnson smashed Azhar Mahmood over long-on for six.
The Irish victory handed Pakistan their second straight defeat in the competition, following their 54-run loss to hosts West Indies last Tuesday.
The win also provisionally puts Ireland in the lead of Group D with three points - one more than West Indies and two ahead of Zimbabwe (both have a match in hand) - leaving Pakistan at the bottom of the table with no points.
West Indies face Zimbabwe on Monday in a match which could make them the first side to reach the Super Eights.
Pakistan contest their final match on Wednesday against Zimbabwe, and the Irish and West Indies close the group stage on Friday.
Niall O'Brien hit a one-day international career best 72 from 107 balls to be the backbone of the Irish chase.
He shared valuable partnerships of 47 with William Porterfield for the third wicket, and 38 with his brother Kevin for the fifth wicket to consolidate for Ireland.
Mohammad Sami was the pick of the Pakistan bowlers with three wickets for 29 runs from 10 overs, and Rao Iftikhar supported with two for 29 from 10 overs.
Ireland had bowled and fielded with purpose in helpful conditions to dismiss the Pakistanis for a modest 132 in 45.4 overs, but they wobbled at the start of their innings.
Jeremy Bray, a century-maker in Ireland's first match against Zimbabwe, was adjudged lbw to Sami for three in the fourth over, and Eoin Morgan was dismissed for two after suffering a similar fate in the sixth over to leave Ireland 15 for two.
Niall O'Brien came to the wicket and took control of the situation to keep Ireland ahead of the scoring rate with Porterfield simply prepared to bat defiantly at the other end.
Porterfield was dismissed in the 21st over however, when Mohammad Hafeez bowled him for 13, but Ireland were already safe, and the equation got easier when a 35-minute stoppage for bad light rain sent the players off the field in the 28th over.
On resumption, Pakistan showed the break had revitalised them, and snared three wickets - including Niall O'Brien - in the space of seven balls to raise hopes of a late fight-back.
Niall O'Brien was stumped off Shoaib Malik in the 34th over, and next over, Rao Iftikhar struck twice to remove Andrew White and Kyle McCallan next ball.
That left Ireland rocking at 113 for seven from 35 overs.
Johnston joined Niall's brother Kevin at the crease and they kept their composure take their side over the line.
Earlier, Ireland, playing in only their second World Cup match ever, got St. Patrick's Day celebrations off to a rousing start, when they won the toss, chose to field, and gutted the Pakistan batting.
Boyd Rankin was the most successful Irish bowler with three wickets for 32 runs from nine overs, Andre Botha supported with the flattering figures of 8-4-5-2, and McCallan collected two for 12 from 5.4 overs.
Only four Pakistani batsmen got into double-figures - Kamran Akmal scored 27, Imran Nazir got 24, Mohammad Yousuf made 15, and Sami gathered 12.
Fall of wickets: 1-7 (Mohammad Hafeez); 2-15 (Younis Khan); 3-56 (Mohammad Yousuf; 4-58 (Inzamam-ul-Haq); 5-66 (Imran Nazir); 6-72 (Shoaib Malik); 7-103 (Azhar Mahmood); 8-105 (Kamran Akmal); 9-130 (Mohammad Sami).
Overs: 45.3 overs
Fall of wickets: 1-7 (Bray); 2-15 (Morgan); 3-62 (Porterfield); 4-70 (Botha); 5-108 (N. OBrien); 6-113 (White); 7-113 (McCallan).
Result: Ireland won by three wickets (D/L Method).
Points: Ireland 2, Pakistan 0.
Man-of-the-Match: Niall OBrien (Ireland).
Umpires: Billy Bowden (NZL) and Brian Jerling (RSA)
TV Replays: Simon Taufel (AUS)
Reserve: Ian Gould (ENG)
Match referee: Chris Broad (ENG)