Ruud, Raul and Robinho retain Real's lead
Goals by Ruud van Nistelrooy, club captain Raul Gonzalez and Robinho produced a slightly flattering scoreline but moved the Spanish giants up to 22 points from their nine games.
Deportivo made a dream start just over a minute into the game when Xisco Jimenez put the Galician side ahead with a right foot shot from 10 yards out.
Real had only themselves to blame after Deportivo goalkeeper Dudu Aouate sent a huge punt forward and the Madrid defenders left Sergio Gonzalez free to pull the ball back to the unmarked Xisco.
However Real were back on level terms barely five minutes later when Ruud van Nistelrooy equalized from the penalty spot after the Dutchman had his legs swept away from under him by Mexican midfielder Jose Guardado.
Having recovered from the early blow, Real then went on the offensive with Sergio Ramos roaming forward to have two good chances only thwarted by the acrobatic Aouate.
Deportivo didn't throw in the though and came out fighting after the break.
Juan Rodriguez and Xisco had good chances early in the second half which could have easily put Deportivo ahead again if it had not been for the skill of Real's Spanish international goalkeeper Iker Casillas.
Real's mid-week two-goal hero Robinho then hit the crossbar with 20 minutes to go before Raul finally gave the reigning Spanish champions the league after 78 minutes, latching on to an inch-perfect pass from the midfield by Jose Maria Gutierrez.
Deportivo then endured further misery two minutes later when Sergio was sent off for his second yellow card and Robinho then got his first goal this season in the league right at the end of regulation time.
Real's local rivals Atletico also had an important victory, winning 1-0 at bottom club Levante to move up to fifth place.
Diego Forlan put Atletico ahead after 36 minutes but the Uruguayan striker will be thanking his team mate Kun Aguero for exquisite service.
Aguero, who himself had two earlier attempts go close, chested down a long Ze Castro pass before laying the ball off for Forlan.
Atletico overwhelmed the struggling Valencia-based side in the second half but Pablo Ibanez, Raul Garcia and Jose Antonio Reyes were all denied by a brilliant display from Levante goalkeeper Marco Storari.
The result means that Levante continue to prop up the Spanish first division and are still looking for their first win of the season.
Real Zaragoza put behind them the internal turmoil of the last week to inflict a 4-1 thrashing on Villarreal.
Brazilian striker Ricardo Oliveira opened the scoring his fifth goal of the season after 36 minutes when he headed home an Alberto Zapater cross.
Oscar Serrano got Zaragoza's second goal four minutes after the break when he slipped away from his marker and finished off a cross from Diego Milito.
Milito and Sergio Garcia then added further goals before Villarreal's French playmaker Robert Pires got a consolation goal nine minutes from time.
Struggling Valladolid threw away their chance of their first win since the opening day of the season when they allowed Osasuna to come back from two goals down and salvage a 2-2 draw.
Defender Alvaro Rubio scored his first goal in the top flight of Spanish football when he hammered home Valladolid's opener from close range after the ball was crossed into the six yard box by Daniel Ngon Kome.
Left winger Jonathan Sesma then added Valladolid's second with a left foot shot six minutes after the break.
However, shortly afterwards Osasuna coach Jose Angel Ziganda sent on his Cape Verde international striker Dady and it proved to be an inspired substitution.
The Portuguese-born player got goals after 72 and 78 minutes to allow Osasuna to grab a point and retain their unbeaten home record this season.