Messi showcased a great level of understanding with Jordi Alba by meeting the left back's low cross first time for the opener in the 13th minute and playing a one-two with the Spain global moments later and slamming the ball into the bottom corner.More news: Recent Insiders Bustle: Costco Wholesale Corporation (COST), MGIC Investment Corporation (MTG)
Luis Suarez added the fourth before half-time after a terrible back-pass by Pione Sisto left him with only the goalkeeper to beat, and Ivan Rakitic headed home from Ousmane Dembele's corner late on.
Ivan Rakitic added his name to the score-sheet late on as Barca eased into the final eight of the competition.
15' GOAL! Barcelona 2-0 Celta Vigo (3-1 on aggregate): Barcelona and Messi have scored a quick-fire second goal! "They look for each other and are happy to do so, because it is not just Alba assisting Messi".More news: Airtel Broadband Users Can Avail Free Amazon Prime Membership for One Year
Celta had drawn 2-2 at Barcelona in La Liga last month and had gone into Thursday's match after holding Madrid to a 2-2 draw in the league last weekend.
Zinedine Zidane's Real laboured to a 2-2 draw with Numancia on Wednesday to progress to the quarter-finals 5-2 on aggregate.
Ben Yedder scored from a rebound after a shot by Correa to give Sevilla the lead in the 32nd. Atletico is second and Sevilla fifth. "But I shouldn't say that because it will mean we'll draw them!"More news: Equity indices surge to new highs on global cues, buying support
That happens to be the same scoreline by which the Blaugrana beat local rivals Espanyol when they last met back in September, with Lionel Messi contributing a hat-trick along with goals from Luis Suarez and Gerard Pique.