Boca Juniors, Gremio and Penarol all won for the first time in the Copa Libertadores this season, while Cruzeiro and Vasco da Gama were still searching for their opening victories.
Argentine giants Boca opened their 2018 account with a 1-0 win at home to Colombian visitors Junior in Buenos Aires on Wednesday.
Boca were held to a scoreless draw by Alianza Lima in their Group Eight opener last time out but they claimed maximum points midweek thanks to Cristian Pavon's 28th-minute goal.
With Carlos Tevez injured, Pavon stepped up in his absence – curling a shot beyond Sebastian Viera from the edge of the penalty area.
Gremio showed no mercy in a 4-0 rout of winless Monagas following a second-half onslaught in Porto Alegre.
After a goalless opening 45 minutes, Brazilian hosts Gremio – held by Defensor Sporting on matchday one – piled on four unanswered goals via Jael, Everton, Luan and Cicero.
Jael opened the scoring with a glancing header at the near post six minutes into the second half, before Everton double the lead 10 minutes later.
Luan sprung the offside trap as he fired low and hard past Alain Baroja with three minutes remaining, while substitute Cicero completed the comprehensive Group One win.
Penarol bounced back from their first-up defeat after accounting for Atletico Tucuman 3-1 in Group Three.
Meanwhile, Cruzeiro and Vasco played out a goalless draw in their all-Brazilian affair in Group Five.