A Rafinha double coupled with goals from Luis Suarez and Lionel Messi, who came off the bench for his first game after nearly a month out with a groin injury, helped the Catalans cruise to the comfortable win.
"It was a complete performance," said Barca boss Luis Enrique. "We have Leo back and it took him no time to be back in top form.
"Our aim was to surprise them and it worked how we wanted it to. We created lots of chances and they created none. Deportivo have conceded very few goals this season and we got four."
Barcelona have won all four of their most-recent meetings with the Citizens in the Champions League and Enrique feels the match against Deportivo was the perfect preparation to extend that run, but he knows they will be a completely different opponent under Pep Guardiola.
"It is a great way to prepare for a very attractive game for us against an opponent that is continuously improving, and will continue to do so based on what we have seen so far and because of the coach they have," he added.