The Spanish champions already had one foot in the quarter-finals of the competition after coasting to a 4-0 first-leg win, in which Messi also scored twice.
And the Argentina forward tormented Luis Garcia's side once again with a goal in each half at Coliseum Alfonso Perez.
Messi converted Cristian Tello's inviting cross to put the Catalan giants in front and then produced a moment of magic to double the lead, finishing calmly after a trademark solo run that saw him leave several players trailing in his wake.
Xavi came on to make his 700th appearance for the La Liga leaders in the second half, but there was a blow for Barcelona earlier in the game as Neymar hobbled off after spraining tendons in his right ankle when attempting to deliver a cross.
The Brazil forward is to undergo scans on Friday and Barcelona, who face Levante in the quarter-finals, will be keeping their fingers crossed that he will not be ruled out for long.
A controversial goal from Javi Ros ensured Real Sociedad progressed to the quarter-finals with a 1-0 victory at Villarreal.
The midfielder struck from close range in the first half, but there was a suggestion of offside and the ball also appeared to have gone out in the build-up to the goal.
A missed second-half penalty from Jeremy Perbet capped a miserable night for the hosts, who would have fancied their chances of going through after a goalless first leg.
Sociedad will now lock horns with Racing Santander, with a place in the semi-finals at stake.
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