Newell's have a three-point lead over River Plate, who beat Independiente 2-1 on Sunday, with two matches to go in the "Final" championship, the second of two in the season.
Newell's coach Gerardo Martino said getting the win was key in order to regain the momentum from Sunday's loss to All Boys.
"This is important because we had to recover from the defeat at All Boys. There's still a way to go, we must win so as not to give River a chance," he told reporters.
Third-placed Lanus, three points further back, hoped to keep pace but their match at Estudiantes in La Plata was abandoned at half-time when they were 2-0 down after a fan was killed in a clash with riot police.
Rodriguez put Newell's ahead after half an hour at their Marcelo Bielsa ground and also netted the fourth in the second half.
Striker Ignacio Scocco added the second just before halftime, netting the rebound after goalkeeper had parried his first effort, to take his tally to 11 as the championship's top scorer.
Defender Gabriel Heinze struck the third at a corner in the 55th minute and substitute Maximiliano Urruti rounded off the rout 10 minutes from time.