But Brazil soon got to grips with the game and opened the scoring in the 25th minute with a fine individual strike from Coutinho.
Liverpool's playmaker picked up the ball on the left, cut inside and drilled an unstoppable effort from 20 yards into the top corner.
Neymar came close to doubling the advantage when he broke away on a counter-attack, but his shot from an acute angle hit the post.
The Barcelona star, who was out-performing his domestic teammate Lionel Messi, did get on the scoresheet in first-half stoppage time with another fine goal -- his 50th in the famous yellow and blue.
It was made by a superb incisive pass from Gabriel Jesus, who set Neymar clear and the finish was cool and into the bottom corner.
Argentina brought on Sergio Aguero at half-time, but his introduction made little difference to proceedings.
Paulinho thought he had made it three just before the hour when he rounded the goalkeeper, but a heroic piece of defending by Pablo Zabaleta saved a certain goal.
But Paulinho had to wait just four minutes to atone for the miss when he swept home from 12 yards after some poor Argentina defending.
Edgardo Bauza's side were a total no show in the second half, with Messi unable to have any impact. Bauza, just four games into the job, could be under threat.
Brazil continued to enjoy total dominance in the final 20 minutes but failed to inflict further damage.
