The Catalan giants netted three times in the first half and twice in the second, with substitute Paco Alcacer failing to convert from the spot late on to extend his side's advantage in the annual competition.
Chape were unable to truly create too many openings in front of goal on what was an emotional evening for the visitors, who sported a specialised shirt featuring 71 stars to represent each of those who perished in the tragic plane crash last year when the team were travelling to Colombia for a Copa Sudamericana match.
Luis Suarez had his own personal battle with Curzel, being thwarted by the Chape keeper on four separate occasions in the first half alone, including late on through a well-struck volley
Barcelona were getting in behind with ease, opening the scoring with six minutes on the clock through a Gerard Deulofeu tap-in following some good work from Rakitic.
Sergio Busquets added the second thanks to a bullet strike from range, picking out the top corner of the net to put Barca well on their way to a convincing victory.
The hosts were able to make the most of the gaps that had opened up at the other end of the field, though, adding a third of the evening via a sweeping finish from Messi on the back of an exchange of passes with returning teammate Deulofeu.
It was then left to Curzel to keep the scoreline down, producing a string of stops to deny Suarez and one to frustrate Andres Iniesta, while Reinaldo also did enough to block a Messi attempt on the line.
Barca took some time to get going in the second half, but once they did so they scored a trademark goal when Suarez this time beat Curzel at his near post from a slight angle, having been picked out by a smart Messi pass.
Ernesto Valverde's men were going through the motions for most of the half with the victory wrapped up by the interval, though they did add a fifth 74 minutes in as half-time sub Denis Suarez tucked past Curzel.
The new Barca boss was given a chance to make widespread changes during the second period, including the introduction of summer signing Nelson Semedo for his home debut.
There was time for Alcacer to miss from the stop, seeing his effort kept out by Curzel after Semedo was brought down in the box, meaning that the dominant hosts had to settle for just the five goals.