Roberto Soldado gave the home side the lead from the penalty spot after Antonio Amaya had been dismissed for Betis, before a late own goal from Junior Paulao and a strike from Jonas made sure of the points which lifts Valencia up to fifth.
Betis saw a three-match unbeaten run ended and they now sit seventh, two points behind Ernesto Valverde's men.
Visiting goalkeeper Adrian was called into action after just nine minutes at the Mestalla, tipping Tino Costa's left-footed drive round the post before Adil Rami's ambitious overhead kick from the resulting corner fell wide.
However, Valencia made the most of their next opportunity when it was handed to them after 16 minutes.
Soldado was brought to the ground in the area by Amaya, a challenge which earned the Betis player a red card. The former Real Madrid striker then picked himself up to take the penalty, picking his spot in the bottom-right corner.
Boasting a man advantage, the home side began to apply the pressure on their opponents' goal with Sofiane Feghouli firing wide and Banega Ever driving left footed over the bar.
Betis' best hopes of an equaliser came at the end of the first half when Etxebarria Benat curled a free-kick high over the mark.
Valencia responded after the restart with a shot from the centre of the area by Feghouli, which brought a superb diving save from Adrian.
The visitors tried their luck with set-pieces but another free-kick from Benat was gathered by Valencia goalkeeper Diego Alves.
Jose Alberto Canas then produced a powerful strike from 20 yards for Betis but was wide of the mark, while Jeremy Mathieu directed an effort over the bar for Valencia as both sides continued to mis-fire.
In the end it was another helping hand from their opponents which brought Valencia their second five minutes from time, with Sergio Canales' teasing cross from the right turned into his own net by Paulao.
And Jonas added some shine to the scoreline in stoppage time with a low right-footed curler from Costa's cross.