Los Blancos led 2-0 at the interval after netting twice in the space of seven first-half minutes, before Kroos rounded off the scoring just past the hour on what was a comfortable night for the capital outfit, who had Sergio Ramos sent off late on.
Guilherme, Fabian Schar and Zakaria Bakkali all made their debuts for Deportivo from the start, while there was a spot in the team for last season's top scorer Florin Andone despite transfer speculation surrounding the forward.
It was Deportivo that had the game's first attempt on target in the sixth minute, but reported Burnley target Andone, after shaking off the challenge of Dani Carvajal, could not find a route past Keylor Navas in the Real Madrid goal.
Andone had another opportunity less than two minutes later after using his pace to break into a one-on-one situation with Navas, but the Los Blancos stopper was on hand to make another smart save.
After a difficult opening five minutes, it was Deportivo that were looking the team more likely to make the breakthrough, with Guilherme just missing the crossbar with a strike from distance as the first period continued to gather pace.
Real Madrid opened the scoring in the 20th minute, however, when Bale poked home from close range after Deportivo goalkeeper Ruben had parried a Luka Modric effort straight into the path of Benzema, who clipped across goal for his teammate to tap into an empty net.
Seven minutes later, Real Madrid doubled their advantage as Casemiro converted a low cross from Marcelo, who had danced past a couple of challenges before putting the ball on a plate for his fellow Brazilian.
Deportivo continued to threaten, however, with Andone heading over the crossbar from close range in the 37th minute, while Bakkali was causing problems for the champions with his pace and trickery in a wide position.
It was Real Madrid, who enjoyed 74% of the possession in the opening half of football, that entered the interval with a two-goal advantage, however, courtesy of efforts from Bale and Casemiro in the space of seven minutes.
Kroos had the first half-chance of the second period after finding space in an advanced area, but the German's effort was deflected wide of the Deportivo post six minutes after the break.
Ramos should have been sent off in the 53rd minute after raising his hands into the face of Deportivo centre-back Schar, but the referee awarded just a yellow card, much to the disbelief of the home side.
Real Madrid ended the game as a contest just past the hour when Kroos found the back of the net with a powerful finish after Bale had delivered a low cross into the German international.
Deportivo came close to registering in the 64th minute after Guilherme found space in a wide position before striking towards goal, but the midfielder's effort smashed off the crossbar as Real Madrid survived a dangerous moment.
Marcelo and Kroos both had opportunities for the champions approaching the final 10 minutes, but neither could find the target as Deportivo just about survived conceding a fourth on what was a difficult night for Pepe Mel's side.
Andone, who was the home team's biggest threat on the night, had another decent chance five minutes from time, but the striker fired straight at Navas.
Andone then had the opportunity to score from the penalty spot in the 89th minute after Carvajal had brought Bruno Gama to the deck with a rash challenge, but the 24-year-old missed the post as Real Madrid kept their clean sheet intact.
That was not the end of the drama, however, with Real Madrid skipper Ramos seeing red in the 92nd minute after picking up a second yellow card following an aerial challenge with Borja Valle.
Next up for Real Madrid is a home game against Valencia next Sunday, while Deportivo will travel to Levante one day earlier.