After La Real, fourth, drew at Mallorca on Sunday, Atletico moved three points clear of the Basque side with their last-gasp victory at Montilivi.
Morata turned home from close range after a corner was flicked on to him by Angel Correa, with Atletico surviving a long VAR check to see if the striker had strayed offside.
Girona, 12th, started brightly and thought they had won a penalty when Stefan Savic handled in the box, but striker Taty Castellanos was offside.
After Atletico’s 6-1 thrashing of Sevilla last weekend, Simeone kept faith in the Memphis
Depay and Antoine Griezmann strike partnership.
The pair combined early on, with Depay teeing up Griezmann, whose efort was saved by Paulo Gazzaniga.
Then Griezmann turned creator and crossed for Depay, who volleyed narrowly over from close range.
Yannick Carrasco also tested Gazzaniga in the first half, playing well on the lef flank and getting forward at every opportunity.
Depay fired another effort over as Atletico took control of the game.
Early in the second half, Griezmann, one of the league’s most in-form players, set up Marcos Llorente, but he too was denied by Gazzaniga.
Atletico appealed for a penalty when Oriol Romeu handled, but the referee spotted Rojiblancos defender Mario Hermoso pushing the Girona midfielder into the ball when watching the VAR replay.
Jan Oblak was called into action for the first time to deny Viktor Tsygankov and then again to deny David Lopez, who tried to lob him from range.
Atletico’s Slovenian goalkeeper made another fine save to deny Rodrigo Riquelme late on, with the on-loan midfielder almost scoring against his parent club.
With the game petering out, substitute Morata intervened late on to snatch Atletico three points from an even clash, their fourth win from their last five La Liga games.
AFP