The 33-year-old converted from the penalty spot after being fouled in the area in the first half.
Players such as Ansu Fati and Philippe Coutinho widened the gap on the scoreboard by drilling two more goals after Messi's initial salvo.
First up, it has been revealed that Ansu Fati has etched his name into the Champions League history books.
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"We go into it with the maximum motivation possible", said Fati. "It's a Clasico, I've always dreamed of competing in it".
"Right now his performances could be better".
It made Barca the first team ever to have two goalscorers aged 17 or younger in a Champions League fixture and it remains to be seen if Griezmann regains his place against Real Madrid this weekend. If Koeman is to succeed in the dugout then he will have to build everything around his captain and help him get back to his prolific best in front of goal.
Messi told the club about his desire to leave after the Champions League 8-2 loss to Bayern Munich in August, but this week they return to European action with renewed hopes.
Kharatin converted the penalty and there might have been a nervy finish if Nguen's shot was not well-blocked by the sliding Clement Lenglet.
Barca were quick to close the door on any Ferencvaros comeback, Pedri sweeping home with eight minutes remaining.