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.
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 half-time, netting the rebound after goalkeeper had parried his first effort, to take his tally to 11 as the championship's top scorer.
