Juan Roman Riquelme finished off a fine team goal to open the scoring for Boca against Union Espanola in Buenos Aires while Vasco's Diego Souza struck a superb individual effort for their second against Lanus in Rio de Janeiro.
Six times champions Boca needed a last-minute goal from Uruguayan striker Santiago Silva, heading home substitute Pablo Mouche's cross, to secure their victory over the Chileans at La Bombonera.
Boca took a first half lead when midfielder Pablo Ledesma sent over a high cross, Silva played it back to striker Dario Cvitanich who laid off for Riquelme to shoot inside the base of the far post.
The Chilean side equalised in the 72nd minute when a poor clearance by the Boca defence allowed striker Sebastian Jaime a free run across the face of goal before shooting past goalkeeper Agustin Orion.
Less than two minutes later, midfielder Walter Erviti almost restored Boca's lead when he darted past three defenders only to see his shot come back off the near post.
Espanola had Uruguayan central defender Diego Scotti sent off in added time for chopping Riquelme down and he will miss next Wednesday's second leg in Santiago.
"At home you always have to win... It's a pity they scored against us," the shaven-headed Silva told Fox Sports.
Jaime said: "(Our) goal is going to be important, we're going to validate it in Chile."
Vasco striker Alecsandro volleyed the 1998 South American champions ahead in the 25th minute at the San Januario.
Midfielder Diego Souza then put the Brazilian side two up just before halftime when he did a 'sombrero', looping the ball brilliantly over a defender at close quarters, and volleyed past goalkeeper Agustin Marchesin.
Uruguayan Mario Regueiro pulled one back for Lanus just past the hour to give the Argentine side an away goal that could be decisive in the return leg in Buenos Aires.
Corinthians successfully defended the only unbeaten record in the competition with a 0-0 draw away to Emelec in the Ecuadorean port city of Guayaquil.
The Brazilian side were a man short for most of the second half after forward Jorge Henrique was sent off in the 52nd minute for a second booking.