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Marcelo Gallardo's side struggled to break down Gimnasia's defence early on, but took the lead 10 minutes before the break through Sebastian Driussi's close-range strike.
"It's always nice to score with this shirt, I think there were many games where I didn't score and luckily we scored three goals," Driussi said.
"We focused more, we had been working well but we were always missing that last bit of space to score. The victory fills us with confidence," the midfielder added.
Driussi set up Franco Mastantuono to double River's advantage after the interval with a neat finish before Rodrigo Aliendro added the third eight minutes from time.
River Plate are third in Group B on 25 points and will face Independiente del Valle in the Copa Libertadores on Wednesday before hosting Boca Juniors in the Argentine derby on April 27.
