Getafe had struggled to find a way into the match but two red cards in four minutes threatened to shift the balance.
First, referee Cuadra Fernandez turned a yellow card into a red for Molina after consulting VAR, the striker catching Thomas Partey late down the back of his heel. Then Lodi was handed a second yellow for planting his hand in the face of Damian Suarez.
Atletico dropped Saul into left back before Felix was sacrificed later in the second half, Mario Hermoso coming on for his debut where Lodi had started.
But not before Felix produced the most exhiliarating moment of the match, for which an otherwise rather muted debut will be remembered.
Collecting the ball in his own half, he slid past one Getafe opponent, nutmegged another and then weaved through two more. After motoring 30 yards, he was finally brought down by Bruno for a penalty, the fans cheering as if they had seen a goal.
It should have been worth one but Morata’s shot was pushed wide by David Soria and Getafe remained in touch.
Getafe kept it close and Morata should have made it two when sent through in injury-time. One was enough.