The Pumas, on the back of one of their best results in the tournament, welcomed the world's number one side and held their own in the first half.
Aaron Cruden replied with his own penalty for the All Blacks but Sanchez fired back almost immediately.
The Argentina kicker then missed a penalty, before the visitors scored the game's first try. Julian Savea collected the ball wide on the left and flew down the wing before going over in the corner. After a video referral, the try was awarded but Cruden missed his kick.
The two teams exchanged penalties once more before going in at the break with New Zealand just ahead.
At the start of the second half there were penalties for each side yet again and both were converted before New Zealand increased the tempo with two good tries.
First Sam Cane forced his way over after sustained pressure from the away side, before an excellent move, starting with a lineout and ending with Ben Smith going down between the posts, put New Zealand in command.
Argentina continued to win several penalties but mainly kicked for touch as they looked to get back into the game.
It was not to be, though, and it was New Zealand who ended on top with Smith going over again to put some gloss on the scoreline and earn his side a bonus point.