Claudio Ranieri's side were in an unstoppable form at the Riazor as they roared into a 4-0 lead at halftime and gave their bemused opponents no chance with their slick, one-touch passing football.
The victory put Valencia a point clear of Real Madrid at the top after four games, although Barcelona could join them if they beat unbeaten Real Zaragoza at home on Thursday.
Real won 1-0 at home to Osasuna on Tuesday thanks to an exquisite free kick from David Beckham, but turned in an otherwise tepid performance in their first game since coach Jose Antonio Camacho decided to throw in the towel.
Atletico Madrid and Espanyol lost their unbeaten records when they slumped to respective 1-0 defeats away to Levante and Getafe on Wednesday and are now three points off the pace.
Malaga claimed a spectacular 4-1 win over Numancia featuring stunning goals from midfielder Miguel Angel and Costa Rican striker Paulo Wanchope.
SPARKLING DISPLAY
But it was Valencia who produced the most sparkling display of the night as they crushed last season's Champions League semi-finalists on their home turf.
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Fellow countryman Marco Di Vaio made it 2-0 just over 20 minutes later when he launched himself at a superb curling cross from Francisco Rufete and scored with his heel as he got to the ball before keeper Jose Molina.
Deportivo did not play badly but they were simply unable to cope with a team that gave an almost faultless exhibition of ruthless attacking football.
The Galicians conceded a third when Vicente cut inside right back Manuel Pablo and sent a shot screaming into the far corner with his supposedly weaker right foot in the 43rd minute.
Ranieri's side showed no mercy as they killed the game off with a fourth before the break.
Baraja spotted Rufete's run from the right, threaded the ball through the Depor defence and the winger rounded Molina before slotting home into the empty net.
There was no let up after the break and Baraja weighed in to make it 5-0 in the 51st minute when he drilled in from close range after the outstanding Di Vaio had got to the byline and cut a great pass back across the area.
Uruguayan striker Walter Pandiani pulled one back for Depor when he slotted home just after the hour, but it was scant consolation.