River Plate entered Sunday's fixture without a win in five matches, including four straight in the Primera Division but their luck looked to have turned when Juan Carlos Menseguez gave them the lead after just eight minutes.
But goals from Roman Martinez and Carlos Auzqui, either side of a red card to River Plate's Cristian Ledesma, ensured Estudiantes led at half-time, and the visitors from La Plata held on in the second half to extend the hosts' winless run.
River Plate remain in 14th position in Argentina's top tier and have fallen 12 points behind leaders Newell's Old Boys, who drew 2-2 with Colon.
At the Estadio Monumental Antonio Vespucio Liberti, Menseguez finished off Ariel Rojas' good lead-up work to give the home fans something to cheer about early but Estudiantes equalised in the 17th minute after River Plate failed to deal with a cross from the left wing.
After River Plate goalkeeper Marcelo Barovero made an initial save, the ball bobbled around in the six-yard box before Martinez poked the ball home.
In the 29th minute, a second yellow card saw Ledesma sent off, before Auzqui put Estudiantes in front with seven minutes until the break, tapping in a cross at the back post after a top move down the left involving Jonathan Silva and Patricio Rodriguez.
The victory took Estudiantes up to sixth on the table with 22 points ahead of Godoy Cruz and Atletico Rafaela.
Godoy Cruz drew 1-1 with Belgrano, while Rosario Central came from behind to stun Atletico Rafaela 3-2.
With Newell's having to fight back for a draw away to Colon thanks to a late brace from David Trezeguet, San Lorenzo moved with two points of the league-leaders with a 1-0 win over Boca Juniors.
Angel Correa scored the goal for San Lorenzo, as they moved up to second above Arsenal, who were held to a 1-1 draw by All Boys.
In other results, Argentinos Juniors thumped Olimpo 4-0, Racing Club won 3-1 away to Gimnasia La Plata and Lanus edged out Tigre 3-2, while Quilmes and Velez Sarsfield played out a 1-1 stalemate.
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