Rodriguez scored eight minutes before half-time to seal a result which took Newell's to 16 points from seven games.
Lanus face Quilmes on Tuesday.
Godoy Cruz stayed hot on their heels as Mauro Obolo scored twice to lift them to a 3-2 win at San Martin San Juan.
Obolo netted after 10 minutes, but Godoy Cruz found themselves 2-1 down before the break thanks to a Nicolas Sanchez own goal in the 21st minute and Damian Ledesma's strike just after the half-hour.
Substitute David Ramirez levelled in the 63rd minute, just moments after coming off the bench, and Obolo grabbed his second eight minutes from time to seal the win.
Morel Rodriguez netted in the 63rd minute to salvage a 1-1 draw against Boca Juniors, who played nearly the whole game with 10 men.
Christian Cellay was sent off in the 16th minute, but Santiago Silva netted six minutes before the break - a lead which held until Rodriguez struck.
Diego Vera's 31st-minute goal gave Atletico Rafaela a 1-0 win over Union Santa Fe.