When Edwuin Gomez converted a penalty for Universitario just before the hour mark, the home side led 3-1 and looked on track to triumph in Peru.
But The Strongest reduced the hosts' margin soon after through Ernesto Cristaldo and the visitors capped off their comeback with Jair Reinoso's last-minute strike.
Reinoso's late heroics appropriately wrapped up a match full of drama and a healthy dose of farce in Group One.
The home side opened the scoring in the 29th minute when Raul Ruidiaz cut inside his marker to finish from close range but Universitario's lead did not last long, as Alejandro Chumacero won a penalty for The Strongest three minutes later.
The home side's goalkeeper Jose Carvallo saved both Pablo Escobar's penalty and his follow-up effort before Nelvin Soliz's shot was blocked on the line. The ball rebounded to Reinoso and, although he could not control it, his poor touch ricocheted off Universitario's Diego Chavez and into the net.
The hosts recovered quickly though, as Christopher Gonzalez thrashed the ball into the net in the 38th minute, and the Peruvian club extended their lead 12 minutes after half-time thanks to Gomez's spot kick.
The Strongest entered the match having lost their previous two away matches in the Copa Libertadores but began to believe they could avoid defeat when Cristaldo got free at the back post to head Escobar's cross home in the 66th minute.
Cristaldo also helped create the equaliser, picking out Escobar in the box and the attacking midfielder spun on the ball, sending a first-time cross to the back post where Reinoso completed a simple finish.
The draw saw The Strongest move to seven points, keeping their hopes of qualifying for the knockout stages alive, as they sit third, two points behind second-placed Atletico Paranaense, who the Bolivians host on the final matchday.
In Ecuador, Independiente del Valle scored an even later equaliser with Junior Sornoza making no mistake from the spot in the fifth minute of second-half stoppage time to clinch a 1-1 draw with San Lorenzo.
Nicolas Blandi's header from a corner had given San Lorenzo the lead in the 58th minute but after defending desperately in Quito, the Argentine visitors eventually conceded when Emanuel Mas almost kicked Independiente's Fernando Guerrero in the head.
The referee awarded a penalty and Sornoza scored with the last kick of the match.
San Lorenzo's furious players then attempted to surround referee Carlos Amarilla to dispute the decision but the local riot police poured onto the pitch to protect the match officials and rather violently pushed the visitors away.
The draw left both teams on five points at the bottom of Group Two with Botafogo top of the standings with seven.
In the other match, Lanus defeated Cerro Porteno 2-0 to go top of a congested Group Two.
Lanus are level on seven points with Cerro Porteno and Deportivo Cali, who are all just one ahead of O'Higgins heading into the final matchday.
