There was no shortage of action early on, as Dimitri Foulquier and Yunus Musah had chances for the hosts, either side of Lucas Ocampos being denied at the other end.
The game soon settled down though, with the tension growing as both teams began to realise the magnitude of the occasion in their respective relegation battles.
Los Che were still largely the aggressors as Edinson Cavani headed off target and Toni Lato saw a shot saved by Marko Dmitrovic.
The two sides were struggling with their final ball though, and in total the two keepers were only forced into one stop apiece before the half drew to a close.
Sevilla were brighter after the break, as Ocampos dragged narrowly wide from distance before Loic Bade controversially bundled home the opener from close range, despite what looked like a foul on Musah.
If that wasn’t bad enough for Valencia, they were left incensed with the officials minutes later when Fernando somehow got away with a clear handball in the box, despite intervention from VAR.
To rub salt into the wounds, Jose Luis Mendilibar’s side doubled their lead with 15 minutes remaining when Suso calmly curled into the bottom corner from the edge of the area.
There was to be no comeback from there, as the visitors, who remain unbeaten in four games under their new boss, move eight points clear of danger.
Meanwhile, Valencia are now on a run of only two wins in 15 league outings and finished with 10 men after Ilaix Moriba was sent off for a foul on Bryan Gil.
