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."
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 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.
