Carlo Ancelotti's side were at their devastating attacking best at the Riazor, with a Gareth Bale double, James Rodriguez's first Liga goal and a late brace from Javier Hernandez supplementing Cristiano Ronaldo's hat-trick.
Defeats to Real Sociedad and Atletico had put Ancelotti under some pressure, but after a morale-boosting 5-1 UEFA Champions League win over Basel on Wednesday, the European champions never looked like falling to a third straight Liga loss.
Real went in three to the good at half-time courtesy of two goals from Ronaldo that sandwiched Rodriguez's superb 20-yard left-foot strike.
Deportivo pulled a goal back six minutes into the second half as Haris Medunjanin confidently converted a penalty - awarded after a Sergio Ramos handball.
But any hopes of a comeback were dashed by Bale, who restored Real's three-goal advantage with 24 minutes to go.
Bale doubled his tally in the 74th minute and Ronaldo completed his treble soon after, before on-loan Manchester United striker Hernandez came off the bench to add further gloss to the scoreline after Toche had grabbed a consolation for the hosts.
After four rounds Real are three points adrift of league leaders Barcelona, who are due to play Levante on Sunday, while the Madrid club are within two of city rivals and defending champions Atletico.
Atletico missed the chance to go top, albeit temporarily, after drawing 2-2 at home to Celta Vigo.
The Spanish champions were beaten 3-2 by Olympiacos in the Champions League on Tuesday, and their disappointing week continued as Celta earned a share of the spoils.
Pablo Hernandez gave Celta the lead with an outrageous finish after 19 minutes, but Atletico were ahead at the break courtesy of goals from centre-back pairing Miranda and Diego Godin.
However, Miranda undid his good work by giving away a penalty early in the second half, which was subsequently converted by Nolito.
Atletico piled the pressure on in the latter stages, forcing Celta goalkeeper Sergio Alvarez into several saves before substitute Alessio Cerci had an injury-time goal disallowed for offside, but they had to settle for a point in the final game of coach Diego Simeone's touchline ban.
Granada are level on eight points with Atletico after they stunned Athletic Bilbao 1-0 away from home.
Jhon Cordoba's first-half strike was all that separated the two teams at San Mames.
Cordoba struck six minutes before half-time, firing the ball between Iraizoz's legs as Bilbao crashed to back-to-back Liga defeats.
Meanwhile, Espanyol remain in the relegation zone after conceding an injury-time goal to draw 2-2 at home to Malaga.
Espanyol held a 1-0 lead at half-time thanks to Felipe Caicedo, before Ignacio Camacho hit back for the visitors eight minutes into the second half.
Uruguay international Christian Stuani thought he had netted the match-winning goal two minutes from time, only for Malaga to hit back through substitute Duda with the final kick of the game.