Striker Nicolas Blandi tapped home from two metres in the 59th minute after midfielder Cristian Erbes' cross bisected the two central defenders.
Six times champions Boca, struggling in their domestic league, won for the first time in six matches more through grit and experience than good play.
World club champions Corinthians, who won their first Libertadores Cup beating Boca in last year's final, had two good chances to equalise soon after the goal.
Boca goalkeeper Agustin Orion made a diving save to deny Romarinho in the 63rd and Peru striker Paolo Guerrero hit the post six minutes later.
The Argentine side's midfielder Pablo Ledesma had the ball in the net again eight minutes from time but it was ruled out for offside.
Ledesma then picked up two bookings in succession, first for taking off his shirt to celebrate before realising his goal was invalid and then for a foul on Ralf, and was sent off.
"In this matter of two legs it's good to score an away goal. We lost but it was good to have conceded only one. We can turn this round at home," Corinthians midfielder Danilo told reporters.
Boca will be hoping playmaker Riquelme has fully recovered from a thigh injury for the return match in Sao Paulo in two weeks.
Brazilian former champions Gremio, without suspended coach Vanderlei Luxemburgo, beat Independiente Santa Fe of Colombia 2-1 at home in Porto Alegre despite being a man short for more than half an hour.
Chile striker Eduardo Vargas put the home side in front with a header from Alex Telles's cross in the 28th minute at the new Arena do Gremio.
Argentine midfielder Omar Perez equalised for Santa Fe with a penalty early in the second half after centre-back Cris brought down Jefferson Cuero and was sent off for the second time in the competition before Fernando gave Gremio victory 10 minutes from time with a low drive from 25 metres.
Luxemburgo was banned for six matches for his part in a brawl at the end of Gremio's last group phase match, a 1-1 draw away to Chile's Huachipato two weeks ago.
The former Real Madrid and Brazil coach, who will only be able to sit on the Gremio bench again if they reach the final, was alleged to have sparked the brawl by making fun of eliminated Huachipato.
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