Newell's won 1-0 away to Racing Club to stay one point ahead of San Lorenzo in the Argentine top-flight while Argentinos Juniors' poor run continued.
Rodriguez scored a stunning goal versus Racing, his third in four games for Newell's to go with his international goal for Argentina earlier in the month.
Racing, who sit bottom of the Primera Division, looked on track for an unexpected point against Newell's until Rodriguez intervened in the 86th minute.
The 32-year-old winger picked up the ball around 25 yards from goal on the right-hand corner of the box, went past four Racing defenders on a slaloming run and then slotted his shot inside the near post.
The victory took Newell's to 17 points from eight games this season, while San Lorenzo moved up to 16 after a 2-0 victory on the road at Colon.
After a goalless first half at Colon's Estadio Brigadier General Estanislao Lopez, Ignacio Piatti put San Lorenzo in front in the 66th minute with a thumping strike from 25 yards.
Just six minutes later, the visitors doubled their lead when Hector Villalba stole possession on the left wing, burst forward and then slipped the ball into the middle where Juan Ignacio Cavallaro finished from close range.
Arsenal dropped to third after they were held to a 1-1 draw by Rosario Central, which allowed San Lorenzo to claim second.
Gimnasia La Plata and Argentinos Juniors sit just below Arsenal on goal difference with all three clubs on 14 points.
Estudiantes held Gimnasia to a 1-1 draw, while Argentinos Juniors failed to win for the third game in their last four after a scoreless stalemate versus Boca Juniors.
In Buenos Aires, Velez Sarsfield thumped Atletico Rafaela 4-1 with Lucas Pratto scoring one and setting up another for the victors, while River Plate defeated All Boys 1-0.
In other results, Godoy Cruz won 2-0 over Tigre, Olimpo drew 1-1 with Belgrano and Quilmes were held to a scoreless draw by Lanus.
