Gremio travelled to the city of San Miguel de Tucuman in Argentina and drew first blood in the opening leg of their quarter-final tie thanks to Alisson and Everton.
Alisson broke the deadlock away from home before turning provider for Everton in the second half, after Tucuman substitute Gervasio Nunez was sent off in first-half stoppage time.
Tucuman upstaged Atletico Nacional in the last 16 but it was no match for the champion at Estadio Monumental Presidente Jose Fierro.
Alisson put Gremio ahead in the 35th minute when he latched onto a Cicero header at the back post and volleyed past Cristian Lucchetti.
Gremio made the most of its numerical advantage in the second half, Alisson squaring a ball across the six-yard box for Everton to side-foot home.
The return leg will be held in Porto Alegre as Gremio hosts Tucuman in the first week of October.