All the talk pre-match was about the crowd trouble that marred the clash between the two that was planned to take place at El Monumental back on November 25, but thankfully an entertaining encounter at the Estadio Santiago Bernabeu appeared to pass without incident.
River started well, but Boca grew into the game as the first half went on, with the River back line looking particularly shaky.
Pablo Perez was everywhere in a commanding first 45 as he set the tone for his side and he was the first to really threatened as he forced Franco Armani into a routine save.
The midfielder went close once again on the half-hour mark as Dario Benedetto's free-kick was blocked into his path, but his effort was deflected inches wide of the far post.
As half-time approached, Boca found the breakthrough that their performance deserved, Natihan Nandez producing the perfect pass for Benedetto to race away on the counter, with the experienced striker keeping his cool to evade the attentions of last man Gonzalo Montiel and slide a composed finished beyond Armani and into the bottom corner.
So far, so good for Boca, but things would quickly start to unravel after the break as River came out with the bit between their teeth.
Wave after wave of River attack rained down on the Boca goal, with the pressure eventually telling as Pratto lost his marker to meet a pull-back from the right and fire his side level after nice interplay between Nacho Fernandez and Sebastian Palacios.
There only looked like being one winner form there on in as River continued to dominate, though they were unable to create a gilt-edged chance in the remaining 20 minutes or so.
That saw the game go to added time and Boca's slim hopes of getting a result appeared to disappear when Wilmar Barrios was given his marching orders just two minutes into extra time for a second bookable offence.
Quintero was shooting from all angles at this point and that policy eventually paid off as he rifled River in front with 109 minutes on the clock.
The Colombian received the ball on the edge of the Boca box and thundered a left-footed effort beyond Esteban Andrada with the minimum of fuss to put his side on the brink.
Boca, who went down to nine men when Fernando Gago limped off injured with all three substitutions already made, threw the kitchen sink at their opponents late on, with Leonardo Jara's deflected strike clipping the outside of the post in the final minute, but from the ensuing corner Martinez streaked away on the counter to tap into an unguarded net after Andrada had joined the attack.
The triumph is River's fourth Copa Libertadores success, though they will no doubt be disappointed to have not had the chance to win the title in front of their own fans.