In other matches on Thursday, Argentina's Velez Sarsfield beat Deportivo Quito of Ecuador 1-0, while Atletico Nacional of Colombia and Godoy Cruz of Argentina drew 2-2.
Santos captain Edu Dracena also scored for Santos, which reached nine points from four matches in Group 1. Fellow Brazilian club Internacional and The Strongest of Bolivia have seven points each, while Juan Aurich is yet to earn points and has already been eliminated.
The blackout came as the teams returned from halftime under pouring rain, and it took nearly 30 minutes before the problem was solved.
Defender Edu Dracena opened the scoring from close range in the 15th minute by firing in a left-footed shot after Juan Aurich goalkeeper Diego Penny partially saved a header off a corner.
Brazil striker Neymar sealed the victory in the 59th with a low shot from just inside the penalty area after a pass by striker Borges. It was Neymar's fourth goal in this year's Copa Libertadores.
It was Santos' third straight victory after an opening loss to the Strongest in the high altitude of La Paz.
Juan Aurich, only in its third Copa Libertadores, was without three top players on Thursday—William Chiroque, Julio Caicedo and captain Luis Guadalupe, who was sent off early in the second half of the match in Peru.
Santos will now play at Internacional, while Juan Aurich will host The Strongest.
Juan Manuel Martinez scored in the 89th to lift Argentine club Velez Sarsfield to a 1-0 victory over Deportivo Quito in Group 7.
Martinez took advantage of a ball headed into his path and slotted home a left-footed shot inside the near post from close range.
The victory gives Velez a commanding lead with nine points in four matches. Deportivo Quito has four from four matches. Mexican club Chivas has four points in three matches and Defensor Sporting of Uruguay has three from three.
Velez dominated the match, but failed to finish with Federico Insua and Augusto Fernandez going close throughout the game in the Argentine capital.
In Mendoza, Argentina, Atletico Nacional and Godoy Cruz could not get past a 2-2 draw in Group 8. The result gave Godoy eight points from four matches to lead the group. Nacional has five in four matches.
Nacional took a 1-0 lead in the third minute when Luis Fernando Mosquera capitalized on a defensive error and scored from close range. Godoy Cruz equalized in the 24th off Jorge Curbero's free kick, then took the lead in the 35th with Facundo Castillon's shot from 10 meters (yards).
Mosquera got his second in the 62nd minute, leveling the score with a penalty.
Godoy's Leonardo Sigali was sent off for his second yellow card in second-half stoppage time.