An Alberto Lopo own goal, a sensational overhead kick from Diego Costa and a late Adrian strike sealed an emphatic win for the Rojiblancos
Midfielder Garcia headed in Koke's cross to break the deadlock early on before Arda Turan's delivery was diverted into his own net by Alberto Lopo.
The visitors' task became that bit more difficult when Juan Valera was dismissed for a second yellow card, and Villa duly ended the fixture as a contest when he turned home Juanfran's cross shortly after the break having twice gone close earlier in the game.
Garcia scored his second of the night when he headed home from a Tiago delivery before missing a chance to complete his hat-trick, while Felipe Luis also missed a gilt-edged opportunity.
The goal of the night came from substitute Diego Costa, when he leaped and swivelled to power home an outrageous overhead kick for the Rojiblancos' fifth.
Fellow substitue Adrian Lopez set up Villa for his second, firing the ball across goal to allow the former Barcelona man a simple finish, and the striker added extra gloss to the scoreline when he shot low into the corner after some clever build-up play from Costa and Arda.
The resounding win moves Diego Simeone's side back above city rivals Real Madrid and to within three points of league leaders Barcelona. Getafe remain seventh, level on points with Real Sociedad.