Mir's flicked finish in the 22nd minute squirmed past David Soria and was enough for Sevilla to cut the gap to Madrid to five points, with Sevilla owning a game in hand. Madrid thrashed Valencia 4-1 on Saturday.
Real Madrid will be away in Saudi Arabia playing in the Spanish Super Cup this week, Sevilla will have the chance to reduce the difference to two points by beating Valencia next weekend.
Julen Lopetefui's side appears to be the chief challengers to Real Madrid this season, with Atletico Madrid and Barcelona both well adrift. Sevilla are now unbeaten in six games in all competitions.
Getafe, who stay 16th, were undone by a driving run from Luis Ocampos, who beat both Florentino Luis and Jonathan Silva, before firing in a low cross.
Mir flicked the ball behind his standing leg and Soria was taken by surprise, the goalkeeper allowing the ball to creep through his hands and inside the post.