Julian Alvarez put Argentina ahead in the 49th minute but a combination of inspired goalkeeping from Canada's Max Crepeau and Lionel Messi's surprising lack of precision in front of goal ensured that the underdogs were in the game until Lautaro Martinez settled the contest in the 88th minute.
Backed by a huge support decked out in light blue and white striped shirts, Argentina fully deserved their victory but Canada, ranked 48th in the world, can take plenty of credit for the way they fought with the 15-time Copa America winners.
Alvarez, preferred to Lautaro as Messi's strike partner in attack, had the first opportunity when he charged down an attempted clearance from Ismael Kone and broke away.
But the Manchester City striker took a heavy touch as he bore down on Canada keeper Max Crepeau, who was able to smother the ball.
Messi, who became the most capped player in Copa America history, making his 35th appearance in what is his seventh tournament, then went close to an opener himself but his angled shot from the left flashed just wide of the far post.
While the Argentines were exploiting gaps in the Canadian defence, Jesse Marsch's team were nonetheless competing in midfield and creating some half-chances for themselves.
Alphonso Davies and Liam Millar both had shots blocked inside the box and Tajon Buchanan screwed an effort from a tight angle wide in the 30th minute.
The first true save of the game came in the 40th minute, though, when Alexis Mac Allister's stooping header from an Angel Di Maria cross was well dealt with by Crepeau.
But Argentina needed their goalkeeper, Emiliano Martinez, to be at his very best to ensure they went in on level terms at the interval.
Cyle Larin's cross from the right wing was met with a powerful header from close-range from Stephen Eustaquio but Martinez's sharp reaction save kept the game goalless.
Break deadlock
But it took less than four minutes of the second half for Argentina to break the deadlock -- Messi threaded a pass through to Mac Allister, who was brought down by Crepeau, but before the referee could blow his whistle Alvarez had slotted home the loose ball.
Within moments, there was another chance for Alvarez, but this time denied by the diving Crepeau and Canada could live to fight on.
They did so with more urgency and a little more risk after Marsch introduced winger Jacob Shaffelburg and switched to an attacking 4-3-3 formation.
Suddenly the Argentine defence was under pressure and didn't look at all comfortable as Canada got men forward and exploited the wide areas.
But they were almost caught out with a classic counter-attack as Martinez launched a quick long ball towards Messi, who broke way goalwards but with the crowd expecting to see the eight-time Ballon d'Or winner on target he made a hash of the chance.
His initial effort was parried by Crepeau and although Messi latched on to the loose ball and sought to go round the keeper, his shot was easily cleared by the covering Derek Cornelius.
Incredibly there was another great opportunity for the former Barcelona star to find the target and again he was unable to convert -- cutting in from the right with only Crepeau to beat, Messi opened up his body but slid his shot wide of the post.
Crepeau was at his best again to keep out substitute Lautaro as Argentina struggled to put the game to bed but with two minutes of normal time remaining they did just that.
Messi produced another clinical, defence-splitting pass and this time Lautaro made no mistake, slipping past the advancing Crepeau to make it 2-0.
Argentine coach Lionel Scaloni was pleased with his team's spirit but upset with the temporary grass surface placed on top of Atlanta's artificial pitch.
"We had to dig in and close out the game, which is what it's all about in the end," he said.
"Sometime you can't play your game, as I always say, there are times when the opponent won't let you. In this case it was the opponent and the pitch. We had to play differently and the important thing is that we won," he said.
Marsch was pleased with his team's willingness to go toe-to-toe with the world's best.
"We played fearlessly. I think we learnt a lot from it -- mostly that we can play with these dudes," he said.
