The home side settled for four goals but, in truth, it could have been many more had they brought their shooting boots.
Rafinha netted the first two goals before Luis Suarez made it three on the stroke of half-time.
Messi returned from injury shortly after the interval and he duly notched within two minutes of coming on.
Reduced to 10 men for the last 25 minutes when Laure was ordered off, Deportivo will have been glad to get out without conceding any more goals.
Rafinha's persistence earned Barcelona their breakthrough midway through the first half. He stole possession on the edge of the box before exchanging passes with Suarez and squeezing a shot past Lux in the Depor goal.
The same player doubled the lead on 41 minutes. Gerard Pique's header was well saved by Lux but the ball broke perfectly for Rafinha to convert from close range.
Deportivo would have been keen to get in at half-time but Neymar turned on the style on 43 minutes, as he jinked past two challenges and set up Suarez for a one-touch finish inside the box.
The Uruguayan was withdrawn at half-time with the game all but won, however Messi was unleashed 10 minutes into the second half.
On 58 minutes, Neymar slid the ball into Messi's path and he had the time and space to score Barca's fourth goal.
Laure was dismissed for a poor challenge on Neymar on 65 minutes and while Paco Alcacer and Messi went close in the closing stages, the damage was limited to four goals.