Seamer Ian Butler produced his most memorable display for his country, dismissing Abdur Rehman for two off the game's final ball when Pakistan needed two to win.
Butler, who claimed three for 19 off four overs, conceded nine runs off an excellent final over, leaving topscorer Salman Butt stranded at the other end on 67 in an outcome which will probably end the defending champions' hopes at the tournament.
After losing their first Super Eight match to South Africa by 13 runs at the same ground on Friday, New Zealand will still need to win their final match against England at St Lucia on Tuesday to progress to the semfinals.
They bounced back with a superior bowling performance today, having compiled a moderate 133 for seven after being asked to bat at Bridgetown's Kensington Oval.
New Zealand captain Daniel Vettori, who revived the New Zealand innings with 38 off 34 balls, including two sixes, lauded the work in the field.
"We kept ourselves in with a spirited bowling performance," he said.
"We kept attacking, the bowling changes worked, and it worked for us.
"It was always going to be tough work against the quality of Pakistan spinners, and we knew once we got to 133 we were in."
New Zealand's two selection changes proved fruitful, with Butler and Kyle Mills coming in for Tim Southee and Jacob Oram.
Mills was a touch expensive but took two wickets for 33, including the key scalp of Umar Akmal, caught behind on his first ball.
But it was Butler who was most impressive, stalling the Pakistan run chase and removing Misbah-ul-Haq and Shahid Afridi before his last-over heroics.
Butt swatted fours off the second and fourth balls but could only scramble a bye off the fifth, heaping the pressure on his No 9 Rehman, who struck the ball straight to Martin Guptill at deep square leg, prompting scenes of New Zealand celebration.
Spinner Nathan McCullum conceded just 19 off his four overs in another key contribution.
Earlier, New Zealand's innings struggled for momentum against the tight Pakistan spin-based attack.
Opener Brendon McCullum raced to 33 off 29 balls but lacked support, with Jesse Ryder, Martin Guptill and Ross Taylor all departing cheaply.
He struck up a 40-run partnership with Vettori, before Scott Styris contributed 21 and Nathan McCullum another late cameo with 12 not out.
Vettori was happy to play a series of sweeps and flat-batted hits down the ground to more than double his previous Twenty20 best.
It was New Zealand's first Twenty20 defeat of Pakistan in five matches.
In a tournament of largely one-sided matches, New Zealand have been involved in two nail-biters, including their opening defeat of Sri Lanka off the penultimate ball.
