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.
"It was another difficult game for us but we are now happy with the result. We gave our all," goalscorer Garcia told reporters.
"This is a demanding level and we know we can't afford to make mistakes. We are all working hard and we have a big enough squad to cope."
Valencia offered solid resistance and in a cagey start there was little space for either side to exploit.
Atletico striker Diego Costa had a weak drive blocked by goalkeeper Vicente Guaita but Valencia went closest to breaking the deadlock before halftime with home stopper Thibaut Courtois beating away an effort from Juan Bernat.
Godin put Atletico ahead soon after the restart when he headed in a corner and Garcia then hit the post with a strike from distance. At the other end, Courtois was kept busy and made two fine saves to deny Valencia forward Helder Postiga.
Garcia headed the second goal from another corner with a minute to go before Valencia's Parejo kicked the ball away in frustration and was dismissed for a second yellow card.
Third-tier Racing Santander had earlier put their financial problems aside to knock out top flight Almeria with Mariano Sanz and Ruben Duran giving them a 2-0 win for a 3-1 aggregate success.
(Reporting by Tim Hanlon; Editing by Ken Ferris)
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