The victory lifts Los Che up to fifth in the league table and maintains their chances of a top-four finish this season.
Roberto Soldado put the hosts in the lead in the 39th minute when he found himself at the end of a rebound and made no mistake from just yards out.
Things went from bad to worse for Osasuna in the 58th minute when Alejandro Arribas was sent off for his challenge on Soldado.
Ever Banega turned in the resultant free kick with his right foot to virtually wrap up the points for Valencia.
There was still time for Osasuna to lose another player though, as David Timor was dismissed for a second bookable offence in the 74th minute.