Colombia playmaker Quintero powered in an unstoppable strike from the edge of the area to hand River a 2-1 lead after 109 minutes of the final's second leg before Gonzalo Martinez sealed a dramatic 5-3 aggregate victory with the final kick.
"We deserved this title. It was difficult because Boca are a very tactical side and very physical in terms of winning back the ball. We knew we'd have to fight until the end," Quintero told Fox Sports.
His goal came after Lucas Pratto cancelled out a first-half effort by Boca's Dario Benedetto to send the tie into an additional 30 minutes, with no away goals rule in the final.
Boca suffered a costly blow at the start of extra time when Wilmar Barrios was sent off for a second booking, and River took full advantage to clinch a fourth Copa Libertadores title.
"I got the space, I controlled and I shot. I worked on it and luckily that led to a great goal. Now, we have to celebrate it!" said Quintero.