Barcelona were also victors as an eight-minute hat-trick from Pedro Rodriguez helped them come from 2-0 down to win 5-2 away at Getafe. (Agencies)
Bale's replacement Angel di Maria put Madrid in front with a fine left-footed drive on 28 minutes, but Pablo Piatti headed home an equaliser for the hosts six minutes later.
Cristiano Ronaldo then headed home Di Maria's free-kick put Madrid back in front five minutes before half-time, only for Valencia to level once more when Jeremy Mathieu met Dani Parejo's corner.
However, Madrid were not to be denied as substitute Jese Rodriguez grabbed the winner with a low drive that beat Vicente Guaita at his near post 10 minutes from time.
With Bale sidelined for a second consecutive game by a calf injury, Di Maria had another chance to impress and made his presence felt in style as he controlled Marcelo's cross-field pass before firing past Guaita into the far corner.
Valencia, buoyed by the news earlier in the day that Singaporean businessman Peter Lim may be on the verge of taking over the club, responded almost immediately as the diminutive Piatti found space inside the area to head home Juan Bernat's cross.
Madrid were back in front six minutes later in somewhat controversial circumstances as Ronaldo's goal was allowed to stand despite the Portuguese appearing to be slightly offside as Di Maria delivered a free-kick from wide on the right.
The hosts were level once again, though, just after the hour mark when Mathieu outjumped Sergio Ramos to flick home Parejo's corner.
However, Madrid found the goal they desperately needed to get their title hopes alive as Luka Modric picked out Jese inside the area and his fiercely driven effort slipped through the grasp of Guaita.
Barcelona were also made to work for their victory as goals from Sergio Escudero and Lisandro Lopez had given Getafe a 2-0 lead inside 14 minutes.
Barcelona were also victors as an eight-minute hat-trick from Pedro Rodriguez helped them come from 2-0 down to win 5-2 away at Getafe.