Barcelona's 7-1 win over Osasuna earlier in the night had sent the Catalan giants three points clear, but the two teams are now level on 78 points after a second-string Real Madrid side triumphed in La Coruna.
Real Madrid boss Zinedine Zidane made wholesale changes from El Clasico at the weekend, with the likes of Cristiano Ronaldo, Gareth Bale, Toni Kroos and Luka Modric dropping out, while Sergio Ramos missed out through suspension.
As for Deportivo, Romanian international Florin Andone once again led the line for Pepe Mel's side, while Gael Kakuta and Guilherme were both handed attacking roles, but a thigh problem kept Pedro Mosquera on the sidelines.
Real Madrid needed just 53 seconds to make the breakthrough at the Riazor, and it was Alvaro Morata that opened the scoring after smashing the ball past Deportivo goalkeeper German Lux following a smart pass from Isco.
Marco Asensio had a big chance to double the away side's lead in the fifth minute after breaking into the box once again, but Lux was down to make a smart save as an open start to the match continued to produce opportunities, with a curling effort from Isco just missing the post moments later.
Morata had a wonderful chance to double his tally in the 11th minute after creating some space inside the Deportivo box, but the Spain international could not find a route past Lux, who made another big save, before Asensio hit the outside of the post with a stinging drive two minutes later.
More lacklustre defending from the home side presented Vazquez with another opportunity in the 27th minute, but the Spaniard could not roll the ball past Lux, who then made another wonderful save in the 32nd minute to keep out a close-range strike from Morata.
For all Real Madrid's excellent chances in the first period, Deportivo were back in the match in the 35th minute when Andone converted from close range after Kakuta's shot had fallen kindly for the striker inside the Real Madrid box.
Sidnei came close to drawing the two teams level in the 43rd minute, but it was Real Madrid that scored the game's fourth goal in the 44th minute when Vazquez converted from close range after a Marcelo cross had been blocked into the Spaniard's path.
Deportivo made two changes at the interval, with Fernando Navarro replacing Kakuta, while there was an alteration between the sticks as Przemyslaw Tyton took the place of Lux, who took a blow to the face in the latter stages of the first period.
Marcelo had the opportunity to send Real Madrid into a 4-1 lead in the 55th minute when he found space inside the Deportivo box, but the left-back's goal-bound strike was blocked by Sidnei.
The home side had to make their third change of the match in the 57th minute when Gil limped off the field, and it was on-loan Stoke City striker Joselu that was chosen to provide Andone with some support in the final third of the field.
Real Madrid should have scored their fourth on the hour mark when Asensio burst clear of the Deportivo midfield before feeding Vazquez, but the Spaniard could only send his low effort wide of the post, before Tyton was forced to push a low Morata strike wide moments later.
The pressure was relentless, however, and Los Blancos scored their fourth in the 66th minute when Morata rounded Tyton before picking out James, who could not pass up the chance to double his tally for the night as the Colombian converted from close range.
Joselu had the ball in the back of the Real Madrid net in the 73rd minute, but the offside flag was raised as Deportivo endured another frustrating moment on home soil.
The home side came close to a second once again in the 76th minute when Sidnei met a corner from Alex Bergantinos, but the centre-back headed over the crossbar after Casilla had failed to clear his lines.
Real Madrid were not finished, however, and the away side scored their fifth in the 78th minute when Isco converted from close range after Vazquez had found his fellow Spaniard with a smart cross.
Deportivo had their second of the match in the 84th minute when Joselu headed a Guilherme cross into the back of the net, but that was not the final goal of the contest - Los Blancos substitute Casemiro making it 6-2 late on with an effort from distance.
Next up for Real Madrid, who still have a game in hand over Barcelona, is a home fixture against Valencia on Saturday afternoon, while Deportivo are next in action on Sunday away to already-relegated Osasuna.