The Spanish international struck in both halves to help Diego Simeone's side kick off its campaign on a triumphant note at Coliseum Alfonso Perez, with Antoine Griezmann adding the third for the visitor.
Quique Sánchez Flores could well feel the final scoreline did his side a disservice, but it will be the Rojiblancos who end this opening weekend with a smile on their face at a job well done.
In stifling evening temperatures in the heart of the Iberian Peninsula, this local encounter proved a cagey affair throughout, punctuated by occasional moments of brilliance.
It was one such sublime passage of interplay that saw Atletico carve out their opener, with Morata the recipient of a fluid succession of passes down the middle before planting a low finish beyond David Soria.
Carles Alena returned fire seven minutes out from the interval with a ranged effort just wide of the mark, while Borja Mayoral rattled the crossbar, but otherwise both teams tended towards a more physical kind of encounter.
Getafe remained fiercely competitive however – but when Joao Felix picked off a poor pass from the back to send Morata back through again just shy of the hour mark, the latter effectively sealed the deal.
Griezmann's breakaway finish moments after Mayoral steered a header past the wrong side of the post with a quarter-hour to spare confirmed the victory – and sets the stage for the potential of another great title battle this term.