In his first start since returning from a hamstring injury that caused a two-month layoff, Messi scored off Cristian Tello's cross in the 44th minute and blew past four defenders in the 63rd and then slotted the ball in from a tight angle for 2-0. Messi has 18 goals in 19 games this season; his streak of four world player of the year titles was ended Monday by Real Madrid's Cristiano Ronaldo.
Neymar left with a sprained right ankle in the 22nd minute, after his boot appeared to catch on the grass and he fell while dribbling toward the goal line.
Barcelona will play Levante in the final eight.
Following a 5-1 league loss at Villarreal on Monday, Real Socieded defeated Villarreal 1-0 to win the total-goals series by the same score. Real moves on to face third-tier Racing Santander.
Defending champion Atletico Madrid plays Athletic Bilbao and Real Madrid faces Espanyol in the quarterfinals, with start next week.