Winger Angel Di Maria, striker Carlos Tevez and substitute Sergio Aguero also scored in front of a 55,000 crowd at the Monumental stadium against a Canada side who were overwhelmed at times by the speed and precision of Argentina's attacks.
Midfielder Juan Sebastian Veron sounded a note of caution, however, saying Argentina's Group B rivals Nigeria, South Korea and Greece will provide much stiffer opposition.
GEAR:Check out Argentina's WC shirts
"We managed to open a defence that remained packed at the back and whoever your rivals are that's hard to achieve," second-half substitute Veron told reporters.
"We were patient and then with more space the goals came. It was a practice match with a crowd," added playmaker Veron, who is going to his third finals after 1998 and 2002.
"Before a competition like a World Cup you have to take a match like this carefully, it helps build confidence but at the finals it will be different."
MAXI EFFECT
Diego Maradona's side, featuring reserve centre backs and without the rested Lionel Messi, went ahead after quarter of an hour with a right-footed free kick from Rodriguez.
Just past the half-hour mark he scored again, finishing off a lightning break that demonstrated the strength of Maradona's team on the counter-attack.
The ball came out of defence to Gonzalo Higuain, who laid it off to Carlos Tevez breaking through the middle. Faced with two defenders Tevez passed it to his right where Rodriguez hit a low first-time shot under goalkeeper Patrick Onstad.
Di Maria made it 3-0 shortly before the interval when he surprised the Canada defence by curling the ball inside the far post with the outside of his left foot.
The hard-working Tevez also got on the scoresheet just past the hour from a lay-off in the box by Higuain.
Sergio Aguero replaced Tevez and had only been on the pitch a minute when he took a long pass out to the left, cut inside, wrong-footed a defender and scored the fifth.
"The lads understood what I wanted, there are no friendlies wearing this shirt," said Maradona, who cancelled a post-match news conference.
"The fans can relax, we have good players," he said in a televised interview on the pitch.
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