The home side had the better of the opening exchanges and went on to break the deadlock with 18 minutes on the clock.
Carlos Martins slotted the ball through for Jara, who took one touch before slotting the ball into the bottom left hand corner of the net.
Jara had a chance to double his side's advantage before the break, but he headed wide of the target from close range.
Getafe went in search of an equaliser after the restart, but they were unable to breach the Granada net.
Diego Castro had their best chance when he shot over from just ten yards out with 12 minutes remaining.