Valencia recaptured fourth place in La Liga from Sevilla when Sofiane Feghouli scored the pick of the goals in a 4-0 stroll at home to second-from-bottom Granada on Monday.
Sevilla's 2-0 success at home to Rayo Vallecano on Sunday had edged them ahead in the battle for Spain's fourth Champions League berth, which carries a place in qualifying for Europe's elite club competition.
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Valencia, who missed out on a lucrative place in continental competition last season, crushed a weak Granada side apparently doomed to relegation, with Javi Fuego, Dani Parejo and substitute Alvaro Negredo also on target at the Mestalla.
Algeria forward Feghouli finished off a superb move for Valencia's third goal, curling the ball into the top corner after Negredo's first-time pass sent him clear on the left of the penalty area.
Valencia have 68 points with five games left, two ahead of Sevilla and four behind third-placed champions Atletico Madrid, 3-0 winners at home to Elche on Saturday.
Barca lead on 81 points, with Real Madrid two adrift of their arch rivals in second.
Peter Lim's recent takeover of Valencia has given fans hope the Singapore billionaire's investment will help propel their team back to the top in Spain and make them contenders in Europe again.
They last won La Liga in 2004 under Rafael Benitez having reached consecutive Champions League finals in 2000 and 2001, losing to Real and Bayern Munich respectively.
The club were hobbled by financial problems over the subsequent decade which forced them to cash in top players, including David Villa, David Silva and Juan Mata, to stay afloat.
However, Lim and his representatives have pledged a long-term commitment and some wise spending on players over the summer could lay the foundations for a run deep in the Champions League next term if Valencia secure their place.
