The hosts took a 1-0 half-time lead through Jonas's strike.
Betis' task was made more difficult after the break when Chichu Dorado picked up a straight red card.
It didn't take long for Valencia to make their numerical advantage count as Sofiane Feghouli struck after the hour to double his side's lead.
Roberto Soldado found the net with five minutes to play before Pablo Piatti sealed the win just a minute later.
The visitors were reduced to nine men in the final stages when Jorge Molina was dismissed.