The Argentina win combined with The Netherlands' 2-1 defeat of Ivory Coast to allow both winning teams to advance to the 2006 World Cup Round of 16.
The first half was a clinic on Argentina teamwork, with midfielder Javier Saviola in the middle of all three goals and Serbia goalkeeper Dragoslav Jevric the victim.
Rodriguez' first goal came in the sixth minute when he converted a nice setup from Saviola.
The midfielder set off the play that led to the second goal with a pass to Cambiasso, who gave the ball to Hernan Crespo, who passed it right back to allow Cambiasso a clear shot and Argentina a 2-0 lead at the 31st minute.
Only about 10 minutes later, Saviola stole the ball and, on a long run, weaved through the Serbia defense before giving off to Rodriquez, who finished off the play with his second goal.
Argentina got late second-half goals from Crespo, Carlos Tevez and Lionel Messi in posting the most lop-sided score of the tournament to date.
Group C play is scheduled to be completed Wednesday with Argentina meeting The Netherlands to decide which takes first in the group and Serbia and Montenegro going against Ivory Coast in those teams' final game of the tournament.
Notable deaths of 2014 [PHOTOS]