
The defiant win takes "Los Ches" up to eight from bottom, at the same time as pulling Osasuna down to sixth from bottom.
New coach Voro included in his squad Santiago Canizares, David Albelda and Miguel Angel Angulo, the trio of veterans controversially marginalized by Koeman, who was sacked six days ago.
Indeed Canizares played all match because of injury to Timo Hildebrand - and enjoyed a quiet game.
The match turned on an incident in the 18th minute. Osasuna keeper Ricardo Lopez was harshly adjudged to have pulled down Spain striker David Villa in the box. Ricardo was sent off - and Villa calmly made it 1-0 from the penalty spot.
Seven minutes into the second half, Juan Mata made it 2-0 for Valencia by shooting home a clever Villa free-kick.
Spain winger Joaquin Sanchez eight minutes from time, on a pass from Villa after a rapid counter.
Osasuna left the field complaining about the penalty and the sending-off of Ricardo - and worrying about relegation.
Valencia now have 42 points from 34 games, the same quantity as Getafe, who drew 1-1 at home to fourth-placed Atletico Madrid.
Jaime Gavilan gave Getafe an early lead, only for Sergio Aguero to level for Atletico.
There are three teams on 40 points, just above the relegation zone: Osasuna, Valladolid and Recreativo Huelva.
Valladolid drew 0-0 at home to Almeria, Huelva beat bottom team Levante.
Two points behind this trio are Zaragoza, in trouble after a 1-1 draw away to Espanyol.
Albert Riera gave Espanyol the lead on the hour, Ricardo Oliveira salvaged a point for Zaragoza with a penalty six minutes from time, after Espanyol's Francisco Rufete had handled in the area.
Second-from-bottom, and practically doomed, are Murcia, who drew 0-0 at home to Sevilla on Saturday.
Levante, who have just 25 points, are mathematically down after their defeat in Huelva.
At the other end of the table, Sunday is the day when Real Madrid could clinch their 31st Liga title.
In order for that to happen Villarreal need to fail to win away to Betis - and then Real beat Athletic Bilbao at home.
Real are currently 10 points ahead of Villarreal. Barcelona are third, 11 points behind Real, after Saturday's 2-0 defeat away to Deportivo Coruna.
Atletico Madrid are still fourth after their draw in Getafe, six points behind Barca.
Racing Santander are sixth, two points behind Atletico, after losing 3-1 away to Mallorca on Sunday.
In sixth place, one point below Santander, are Sevilla.