Manchester United and FC Barcelona won away from home, and both will be heavy favorites to advance to the Champions League semifinals next week.
Cristiano Ronaldo and Wayne Rooney scored a goal each to give United a 2-0 win over AS Roma in the first leg of the quarterfinals yesterday. Teenage striker Bojan Krkic scored for Barcelona in its 1-0 win over Schalke.
"We can't take anything for granted, but we definitely feel like we can reach the semifinals," United manager Alex Ferguson said.
The second legs are scheduled for next Wednesday.
Ronaldo scored his seventh goal in eight Champions League matches in the 39th minute, jumping over Marco Cassetti and heading in a cross from Paul Scholes.
The goal was Ronaldo's 36th in all competitions this season.
Roma had several chances to equalize early in the second half at the Stadio Olimpico but couldn't put its shots on target.
Instead, Rooney doubled the advantage, knocking in a loose ball after Park Ji-sung headed a long cross from Wes Brown into the box in the 66th. Roma goalkeeper Alexander Doni got his hands on the ball, but couldn't control it.
"Ronaldo's goal changed the game for us," Ferguson said.
"I thought Roma had some good chances the first 15 minutes of the second half. But there are breaks in a football match and I think they were with us today.