Rodriguez remarkably scored two penalties as Independiente overcame Quilmes 5-3 at the Estadio Libertadores de America in Avellaneda on Saturday.
Independiente's win - their fourth in succession after back-to-back losses - helped the club improve to 15 points from seven rounds, level with second-placed Newell's Old Boys, who edged Olimpo 1-0 on Monday.
On the same weekend that Sao Paulo keeper Rogerio Ceni scored from the penalty spot, fellow glovesman Rodriguez stole the spotlight with two goals of his own.
After Brian Sarmiento put Quilmes ahead in the 10th minute, Rodriguez levelled proceedings 16 minutes later, sending opposing Quilmes keeper Silvio Dulcich the wrong way from the spot.
The 25-year-old was at it again 12 minutes into the second half, firing a penalty low and hard into the bottom corner.
Claudio Riano made it 3-0 with the first of his two goals on the hour-mark, before Quilmes mounted a comeback in the final 19 minutes.
Gonzalo Klusener converted a 71st-minute penalty and Jonathan Zacaria set up a nervy finish with a curled effort inside the area five minutes from time.
However, Independiente sealed the points courtesy of Riano and Federico Mancuello in injury time.
The result came on a weekend that saw River fail to take to the field on Sunday.
Unbeaten River - top of the table on 16 points - were scheduled to play Arsenal but their match was postponed due to torrential rain.
Arch-rivals Boca - 10th in the standings - did manage to kick-off their match at home to Racing Club, before the clash was abandoned with the hosts' leading 1-0 in the 57th minute.
"The match shouldn't have started. The pitch was just as bad when it kicked off," Boca coach Rodolfo Arruabarrena said.
"But the state of the pitch could have produced injuries, in that I agree with the referee."
In other results, Velez Sarsfield missed the chance to move level on points with River after they slumped to a 1-0 loss at Belgrano.
Velez dropped down to fourth in the table after their winless streak extended to three games.
Copa Libertadores champions San Lorenzo climbed off the foot of the table with a come-from-behind 2-1 win at home to Godoy Cruz.
Two goals in the space of five minutes in the second half from Nestor Ortigoza and Martin Cauteruccio cancelled out Leandro Fernandez's opener.
Carlos Luna scored twice as Tigre rallied to rout Rosario Central 4-1, while Defensa y Justicia eased past fellow strugglers Gimnasia La Plata 3-0.
Lanus rose to fifth following their 1-0 win over Banfield.
Silvio Romero's 48th-minute strike helped Lanus to back-to-back wins as Banfield had two players sent off in the closing stages.
Atletico Rafaela also recorded consecutive victories after downing Estudiantes 1-0.
