Los Colchoneros made it three La Liga wins in a row as goals from Godin, Antoine Griezmann and Koke helped them outclass Los Rojiblancos who still seemed to be smarting following their midweek Champions League exit.
Atleti appear to have secured their place in the top four and will now be looking to make a late push to close the 10-point gap on bitter rivals Real at the head of the standings.
With them through to the last eight in the Champions League, Diego Simeone's men still have a shot at silverware and Godin believes they are coming to the boil nicely following Sunday's brilliant display.
He told Marca: "It is at the best moment of the season. With the running of the year and the games that are important, the leadership and strength that we need are appearing."