The Galicians made the most of Athletic Bilbao's 2-1 defeat to Espanyol earlier on Monday (AEDT) to move above the Basques and into the top six, boosting their chances of playing European football next season.
Valencia, meanwhile, were dealt a further blow after exiting the UEFA Europa League on away goals on Friday (AEDT) and lie 14th in the Primera Division table, six points off the relegation zone.
Valencia were fortunate to make it to half-time without conceding as the Galicians created a series of clear-cut chances.
Socceroos goalkeeper Mat Ryan had to scramble the ball off his line after Shkrodan Mustafi deflected a cross off the near post, and the Australia international had to make further saves to deny Guidetti and Daniel Wass.
Socceroos Mat Ryan sracmbles the ball off the line►Caltex Socceroos goalkeeper Mat Ryan plunged the ball out of danger on one occasion but was left helpless as his side buckled under pressure 10 minutes from time.Click learn more for the LaLiga HIGHLIGHTS: Valencia CF 0-2 Celta de Vigo Posted by SBS The World Game on Sunday, March 20, 2016
Valencia improved in the second half but fell behind after 80 minutes as Guidetti latched onto an audacious back-heel by Fabian Orellana to lash home.
Five minutes later captain Mallo finished off the hosts, coasting down the right-hand side and cutting inside to beat goalkeeper Ryan at the near post.
Valencia could have conceded again before the final whistle sounded.
Orellana's attempted chip went just wide of the near post, and then the Chilean struck the woodwork with the goal gaping.
As the whistle approached, furious Valencia fans turned their anger on Neville, chanting "Gary go now".
Elsewhere, goals from Pape Diop and substitute Felipe Caicedo saw Espanyol come from behind to beat Athletic Bilbao 2-1 and move seven points clear of the danger zone.
Javier Eraso had given the Basques the lead after 20 minutes by following up his shot on the rebound after Pau Lopez had parried.