Uche opened the scoring after just 10 minutes and Hernan Perez's brace before half-time put the Yellow Submarine firmly on course for all three points, with Vallecano made to pay for poor finishing.
Uche then scored his second and third after the break to complete the rout, with Nery Castillo's double - the second from the penalty spot - for the home side proving mere consolation.
It was the ideal start to 2014 for Villarreal, who suffered back-to-back defeats before the winter break.
Marcelino's men looked completely rejuvenated, albeit against a side that have not won in the league since November 9 and who now lie above only beleaguered Real Betis in the standings.
It was actually Vallecano who started brightly, with Villarreal goalkeeper Sergio Asenjo forced to brilliantly tip away Alejandro Galvez's 25-yard free-kick.
Yet the visitors went ahead with their first real sight at goal in the 10th minute when Uche stole in to tap home from Jeremy Perbet's cross from the left.
The provider turned goalscorer just two minutes later when Frenchman Perbet netted from close range following Tomas Pina's left-wing cross.
To their credit, Vallecano refused to give in and Asenjo was forced to make another wonderful save, this time from Saul, while their luck was summed up when Jonathan Viera struck a post.
Alhassane Bangoura's effort from just outside the area was tipped round the post by Asenjo, while midfielder Adrian headed over.
Villarreal rode their luck and then punished their opponents for their profligacy once again four minutes before half-time, with Perbet once again coolly slotting into the net from close range after a pass from Moi Gomez.
Any hopes of a comeback were quickly dismissed in the 57th minute when Uche finished from Javier Aquino's centre, while the Nigerian completed his hat-trick eight minutes later by tapping in the rebound after Vallecano keeper David Cobeno could only parry Manu Trigueros' 25-yard free-kick.
Vallecano reduced the arrears when Castillo finally breached Asenjo's goal with his effort from Viera's cutback.
The Mexican striker then ensured a measure of pride for battling Vallecano in the final minute when he slotted home from the penalty spot after Uche had fouled Roberto Trashorras in the area.