Guarani matched their rivals in a competitive opening period but the home side found a higher gear after the break.
Gabriel Mercado got the opener after 59 minutes when he seized on a knock down from a corner to fire the ball home from close range.
Rodrigo Mora got a second 13 minutes later when he beat the offside trap and then lifted a sublime chip over the keeper.
"The result was fair and it allows us the chance to go to Paraguay with a two-goal advantage without losing any goals," River Plate coach Marcelo Gallardo said.
"We were imprecise but we didn't give up and we were rewarded for keeping plugging away."
"The tie isn't over but it gives us the tranquillity to go to Paraguay with a favourable result."
River Plate are aiming to win the competition for a third time, while Guarani have never won South America's equivalent of the Champions League.
The Buenos Aires club had the poorest record of all 16 group qualifiers with just one win in six games but they have shown some steel since, eliminating city rivals Boca Juniors and then beating Brazilian side Cruzeiro 3-0 away from home.
The winner of next Tuesday's tie in Asuncion will play either Internacional or Mexican side Tigres in the final.
The two teams play their first leg in Porto Alegre on Wednesday.
(Writing by Andrew Downie; Editing by Greg Stutchbury)
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