The victory, including a late penalty save by Boca goalkeeper Agustin Orion, was sweet revenge after the Brazilians' 2-1 over the Argentine side in Buenos Aires last month and robbed the visitors of their perfect record.
Fluminense lead Group Four with 12 points, two more than Boca who could still take top spot in the final group matches next week when Flu visit eliminated Arsenal and Boca host Venezuela's Zamora, who sit bottom on one point.
"We're going to go for first place in the group," Boca coach Julio Cesar Falcioni told broadcasters Fox Sports.
Boca went ahead just past the half hour when centre-back Leandro Euzebio's poor clearance of a high ball into the Fluminense half fell to striker Dario Cvitanich, who shook off midfielder Diguinho and shot past goalkeeper Diego Cavalieri.
Fluminense were awarded a penalty in the dying minutes when tricky winger Wellington Nem was brought down by Rolando Schiavi but Orion read substitute striker Rafael Moura's intentions and made a diving save to his left.
"We were annoyed we hadn't taken anything from the match at home when they scored from their two only chances there," Orion said.
Brazil's Corinthians secured their last-16 berth with a 3-1 away over Nacional in Asuncion to top Group Six and at the same time eliminated their Paraguayan opponents.
The result qualified Mexico's Cruz Azul, who could snatch top spot if they beat Nacional and Corinthians, who are three points ahead, lose their last match at home to Venezuela's Deportivo Tachira next week.
Argentina's Velez Sarsfield, champions in 1994, secured their place in the next round as Group Seven winners on 12 points with a game to spare after a clinical 2-0 away win over Guadalajara on unfamiliar Astroturf at the Omnilife.
Second place in the group will be decided next week when Ecuador's Deportivo Quito, who have seven points, are at home to Guadalajara and Defensor Sporting of Uruguay, on six points, visit Velez in Buenos Aires.
