Madrid were without suspended talisman Cristiano Ronaldo for the trip to the Riazor, but it made little difference to the European champions as they reclaimed their familiar place atop the standings at the end of the opening weekend.
Bale notched the opener in the 20th minute and another close-range tap-in, this time from Casemiro seven minutes later, saw Madrid in control before the half-hour was up.
Bale then assisted Toni Kroos for Madrid's third goal just after the hour to complete the scoring, although there was still time for some late drama with Depor striker Florin Andone missing a penalty before Madrid saw captain Sergio Ramos sent off.
While Madrid ultimately ran out comfortable winners, it might have been a very different story had Andone made the most of his numerous chances - including two gilt-edged opportunities early on.
Twice in the opening seven minutes Andone got in behind the Madrid defence, but both times he was denied by fine saves from Keylor Navas.
The second of those two Navas saves resulted in a corner from which Zakaria Bakkali probably should have scored from as well, but he headed over from six yards out - and Madrid never looked back.
Zinedine Zidane's men looked menacing going forward from the outset and they made the breakthrough they had been threatening 20 minutes in.
Ruben spilled a Luka Modric shot and Karim Benzema's touch took it away from the Depor goalkeeper and a defender, and allowed Bale the simplest of finishes into an empty net.
Brazil internationals Marcelo and Casemiro then combined to double Madrid's lead soon after, the midfielder side-footing home the fullback's low ball to the far post to finish off a well-worked team goal.
Madrid, who have already added two more trophies to their bulging collection this month after beating Manchester United in the UEFA Super Cup and Barcelona in the Spanish Supercopa, continued to push for further goals after the break, but Depor looked dangerous going forward as well.
And they came close to pulling a goal back in the 59th minute when Andone saw his glancing header cleared off the line by Ramos, who might have been lucky to still be on the pitch after only picking up a yellow card after an incident with Fabian Schar not long previously.
Ramos would end up having an early bath after his stoppage-time red, but Madrid had killed the game off long before then after notching a third goal through Kroos in the 62nd minute.
Bale laid the ball back to the Germany midfielder on the edge of the box and his first-time shot flew past Ruben with the aid of slight deflection.
Madrid were deservedly on course for victory, but Depor merited at least a consolation goal and they nearly got it when Guilherme Torres struck the crossbar.
To cap a hugely frustrating night for Andone, he was then denied twice more by Navas in the closing stages, the second time from a mis-hit penalty in the 89th minute.
Madrid's night also ended on a sour note when Ramos was sent off after picking up a second yellow card after an aerial challenge with Borja Valle, but the points were already in the bag.