Mohammad Rizwan and Babar Azam keep Pakistan alive at T20 World Cup
Knowing defeat would condemn them to a shock first round exit, Rizwan and Babar put on a match-winning second-wicket partnership of 63 as Pakistan reached their target of 107 with 15 balls to spare.
Opener Rizwan finished undefeated on 53 off 53 balls with two fours and a six for his 29th T20 international half-century while Babar made 33 off as many balls with one four and a six.
The victory came after the 2009 champions and runners-up in 2022 had lost both their first two Group A fixtures.
A stunning super-over humiliation at the hands of the United States was followed by a six-run loss to bitter rivals India in a game where they failed to chase down a modest 120-run target.
However, Tuesday's win at the same Nassau County International Stadium where they came up short against India may still not be enough to secure a place in the second round Super Eights.
Pakistan have two points with one game left while India and the United States both have four points from two wins apiece and remain favourites to progress to the next stage.
Despite the loss, Canada, with two points from three games, are still in the hunt for a Super Eights spot.
Dilon Heyliger took two of the Pakistan wickets to fall, dismissing recalled opener Saim Ayub for six and claiming the prized wicket of Babar, both men caught behind.
Earlier, Pakistan restricted Canada to 106-7 despite opener Aaron Johnson hitting his sixth international fifty.
Johnson demonstrated his attacking intent from the start, cracking successive boundaries off the first two balls he faced from Shaheen Shah Afridi.
The Jamaican-born 33-year-old opener made 52 off 44 balls with four boundaries and four sixes before he was eventually out in the 14th over with the score on 73-6, clean-bowled by Naseem Shah.
Johnson was the only batsman in the top six to reach double figures as Pakistan's seamers took wickets on a regular basis.
Mohammad Amir clean-bowled Navneet Dhaliwal (four) with a 141 km/h delivery which sliced through the defences of the opener.
Shaheen recovered from conceding 10 runs off his first over to get rid of Pargat Singh (two) before Nicholas Kirton (one) was run out by a superb throw by Imad Wasim.
Haris Rauf sent back Shreyas Movva (two) - for his 100th wicket in the format - and Ravinderpal Singh (nought) in the space of three balls as Canada reached 55-5 after 10 overs.
Once Johnson was out, Canada struggled to press the accelerator and had added just 14 more runs off 20 balls when skipper Saad Bin Zafar (10) top-edged Amir to Rizwan behind the stumps.
Amir finished with 2-13 while Rauf claimed 2-26.
