The club paid tribute to former player and manager Luis Aragones, who sadly passed away on Saturday, and striker David Villa opened the scoring in the 38th minute before dedicating the strike to his former manager.
Diego Costa's 25th goal of the season in the 72nd minute gave them breathing space, and Miranda's header soon after put the result beyond any doubt.
Brazilian Diego came on for his second debut after re-signing for Atletico and hammered in a late fourth to round off a perfect night for Diego Simeone's side.
Real Madrid couldn't keep pace with their city rivals as they drew 1-1 at Athletic Club in a bad-tempered game that saw Cristiano Ronaldo sent off.
Jese Rodriguez opened the scoring in the 65th minute on his first La Liga start but they were pegged back eight minutes later through Ibai Gomez's thunderbolt.
Ronaldo clashed with Bilbao's Ander Iturraspe and was dismissed for raising his arms with 15 minutes to play.
The result leaves Carlo Ancelotti's men level on points with Barcelona, and both are three behind Atletico.
Elsewhere, Elche moved four points clear of the relegation zone with a 1-0 win over Almeria.
Cristian Herrera's third goal of the season - which came just before the hour-mark - was the difference between the sides, and although Damian Suarez was sent off late on, Elche held on.
Real Betis remain bottom of La Liga but their 2-0 win over Espanyol gave them a first league victory since September.
Ruben Castro's late brace gave Betis a much-needed boost after 14 league games without a win.
