A Mikael Lustig own goal put Argentina ahead after only three minutes before Jonas Olsson equalised in the 17th minute.
Sergio Aguero put the South Americans ahead again and Gonzalo Higuain made it 3-1 in the 23rd minute.
Rasmus Elm netted Sweden's second goal in the 94th minute with a fine free-kick, but it was too little too late to deny the Argentinians.
Argentina scored with their first attack of the game following a fast-flowing move which saw Lionel Messi pass to Angel Di Maria who in turn laid the ball to Higuain and his shot took a deflection off Lustig as it flew into the net.
The hosts looked to test Argentina in the air and Zlatan Ibrahimovic and Kim Kallstrom both came close to converting before Olsson did level the scores, the West Brom defender beating Federico Fernandez to head home.
However, Sweden's joy was short-lived as just two minutes later they were behind again.
Di Maria found Aguero who appeared suspiciously offside but the Manchester City striker made the most of his chance as he fired over goalkeeper Andreas Isaksson to make it 2-1.
Not long after it was 3-1 as Isaksson was unable to hold Messi's shot from outside the penalty area and Higuain pounced to extend Argentina's lead.
The visitors then took their foot off the gas, although Sweden did not make it hard for them as they continued to play with only Ibrahimovic up front.
Sweden had more possession after the break and again tried to unlock Argentina with aerial balls but the match drifted in the last 30 minutes as the game petered out.
Only in the fourth minute of injury time did Sweden close the gap, with a fantastic free-kick by Elm that gave visiting keeper Sergio Romero no chance.
Aguero said: "We're happy because we played a good match and it's always good to start the year in the best way.
"We scored the first one very quickly and that gave us peace to manage the ball.
"And as soon as they equalised I scored to put us ahead again, so that was important too.
"We expect to continue this way, we always dream of big things in the national team."
Team-mate Javier Mascherano bemoaned the late Swedish goal, but underlined the progress made by the Argentinian team.
He said: "It was a good match; it's a pity they scored the last goal, which hides the big difference we had over them.
"But apart from the scoreline we have to analyse the match itself, and we had the ball, we controlled the game and we didn't suffer that much in defence as in other matches.
"The worst thing was the aerial balls, but it's logical because they have tall players and we knew that would be a problem.
"That's why we avoided conceding too many fouls next to our box, and I guess we did that right."