Two goals late in the first half from Roberto Soldado and Ricardo Costa gave the hosts a comfortable lead and the second half became a formality after Alejandro Arribas was sent off and Ever Banega scored from the resulting free-kick.
David Timor then also saw red and Jonas added to the visitors' pain by scoring a penalty in injury time.
The win put Los Che to within two points of Real Sociedad in fourth place, but the Basques can extend that lead when they travel to Getafe on Monday night.
Osasuna, in contrast, remain firmly in the relegation fight.
Valencia got an early scare when Osasuna forward Kiko Sola attacked down the left wing and put in an weak cross which Jeremy Mathieu attempted to clear but only succeeded in diverting narrowly wide of the far post.
The hosts took a while to get into the game.
Soldado had their first attempt, but volleyed into the side netting from a difficult angle, while Jonas later narrowly failed to get his head on a cross from Andres Guardado.
Valencia's best chance of the half came after 25 minutes.
Tino Costa sent a free-kick toward the far post and Jonas got a head on it, but Osasuna goalkeeper Andres Fernandez made a brilliant save to prevent the ball from going in the bottom corner.
Ernesto Valverde's side eventually took the lead six minutes before the break.
Jonas went for goal from the edge of the area and this time Fernandez could only spill the ball and Soldado reacted quickly to get there first and tap into an empty net.
Valencia got a second minutes later when Ricardo Costa made a diagonal run across the area to head home a free-kick from Tino Costa.
Although the hosts' lead was deserved, Osasuna had not made things easy for them, but that all changed in the second half.
Within five minutes Mathieu could have extended Valencia's lead, but the centre-back failed to get a strong enough contact on a cross from Jonas when he was just two yards from goal.
Just before the hour mark things went from bad to worse for Osasuna.
First Arribas was sent off for bringing down Soldado on the edge of the area when the striker was through on goal.
Banega rubbed salt into the wounds by smashing the free-kick in off the underside of the bar, leaving Fernandez helpless.
The visitors were then reduced to nine men, Timor picking up two bookings in the space of six minutes.
And their misery was complete when full-back Nano handled the ball in the area to give away a penalty, which Jonas tucked into the bottom corner with the last kick of the match.