Gremio had marginally the better of the first half and should have gone in front in the 23rd minute when Argentine striker Maxi Lopez robbed defender Thiago Heleno to go one-on-one with goalkeeper Fabio, but shot against the post.
"It could have been 8-4," Cruzeiro coach Adilson Batista said. "We gave away a chance that Maxi spoilt, but we also missed some goals.
"Cruzeiro could have had a fourth goal. We must give credit to the players for their dedication, The Libertadores is not easy," he told reporters.
Playmaker Wagner increased the home side's lead less than two minutes into the second half. Receiving the ball at a short corner, his shot from the right deflected off defender Tcheco into the net.
With 11 minutes to go, Gremio won a free kick in front of goal and Souza's shot dipped over the wall and inside Fabio's left-hand post.
Gremio coach Paulo Autuori regretted his team's missed chances in the opening half hour and said his team would have to improve their finishing for next week's return match at the Estadio Olimpico stadium in Porto Alegre.
"The hardest part is coming here and taking the stance the Gremio team took, playing in our opponents' half," he said. "We didn't let Cruzeiro play, but you can't afford to waste all that effort."
"Sincerely, I have the impression at the moment that if the game at the Olimpico is played in the same way, we have real chances of winning, but we have to score the goals we missed here."
