The Catalan club on Thursday night defeated Celta Vigo 5-0 at home.
Ivan Rakitic added fifth for the defending champions three minutes from time.
Messi again showed his special understanding with Jordi Alba by meeting the left back's low cross first time for the opener in the 13th minute and moments later played a one-two with the Spain global and slammed the ball into the bottom corner.
Having sealed a 1-1 draw in Balaidos in the first leg, Barcelona go into the tie as the favourites to progress, but Valverde insisted his team will not be thinking about their away goal when the match kicks off. The first Barcelona goal was a result of poor goalkeeping by Alvarez while the second was a fine team goal.
Barca's new record signing Philippe Coutinho - out for three weeks with a thigh injury - was also present as the former Liverpool attacker met his new team-mates. Messi then turned provider, lobbing a ideal pass behind Celta's back line to meet the run by Alba, who chipped Alvarez to score. "Messi also creates goals for Alba". Pione Sisto made a catastrophic one after half an hour, as his slack back pass was pounced upon by Suarez, who finished emphatically.
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Bjorn was hoping his side would bounce back in the foursomes after a surprise 2 ½-3 ½ loss to Arjun Atwal's team in the four-ball. Ross Fisher Tyrrell Hatton bt S.S.P Chawrasia (Ind) & Anirban Lahiri (Ind) 5 &.
Celta drew 2-2 in the Camp Nou in the Liga Santander earlier in the season and held Real Madrid to a 2-2 draw on Sunday and could have posed Barca problems.
Two derbies feature in the Copa del Rey quarterfinals, with Barcelona facing Espanyol and Real Madrid taking on Leganes.
2-0 up in the match, Barcelona did not push much in the second half but Paulinho tapped in the ball in the extra time to score his seventh goal in the league.
Sevilla beat Cadiz 2-1 with goals from Wissam Ben Yedder and Joaquin Correa to advance 4-1 on aggregate.