Atletico, fresh from a draw with Barcelona at the weekend that kept them level on points with the champions at the top of La Liga, are still chasing titles on three fronts with their Champions League campaign resuming next month.
The two sides cancelled each other out in the first half at the Calderon but six minutes after the break Godin nodded home and Garcia added a second to give the holders victory.
Valencia's Daniel Parejo was dismissed for a second yellow card in added time of the last 16, second-leg clash.
Real Madrid, who lost to Atletico in last year's final, will try to book a place in the last eight at Osasuna on Wednesday with the cushion of a 2-0 home win before Barcelona visit Getafe on Thursday following a 4-0 victory at the Nou Camp.
- Sports & Recreation
- La Liga