Following on from similarly big victories by Real Madrid and Barcelona in the Champions League, Villarreal stunned the Dutch league leaders with goals from Nilmar (two), Carlos Marchena, Borja Valero and Giuseppe Rossi.
Twente pulled a late goal back through Marc Janko to give them a glimmer of hope for the second leg but Villarreal remain overwhelming favourites to progress.
There was little sign of what was to come as the first 22 minutes of the match passed with little incident.
However, after a slow start, Villarreal took the lead with their first real opportunity through Spanish World Cup winner Marchena, and they never looked back after that.
The deadlock was broken when Valero's corner was flicked on at the near post by Jose Manuel Catala and Marchena, standing unmarked three yards out, had the simple task of heading into an empty net.
That goal sparked Villarreal into life and they had a great chance to make it 2-0 in the 34th minute when Nilmar got in behind the FC Twente defence, but the Brazilian's chip over goalkeeper Nikolay Mihailov came back off the near post.
Villarreal did double their lead in the 43rd minute, though, when Valero latched onto a through-ball from Santi Cazorla and coolly slotted a low shot past Mihailov.
It was to get even better for the home side before the break as they added a third goal through Nilmar following a poor defensive header from Peter Wisgerhof.
Wisgerhof attempted to clear a Villarreal throw but his header went up into the air before falling perfectly for Nilmar to nod past Mihailov.
That was an awful way for shellshocked Twente to end the half, but they had an opportunity to pull a goal back at the start of the second half after Theo Janssen picked out Bryan Ruiz's unchecked run into the box.
However, Ruiz was unable to take advantage as he headed wide while the Villarreal defence appealed in vain for offside.
The Yellow Submarine were far from impressed the flag had not gone up, but they were much happier moments later as Rossi made it 4-0 with a brilliant finish.
The Twente defence stood off the Italy international as he made his way to the edge of the area and the striker made them pay as he curled an unstoppable shot into the top corner with Mihailov motionless.
That was not the end of Villarreal's scoring either as, after Cazorla had tested Mihailov and Twente substitute Janko had fired over at the far post, the Spaniards made it 5-0 in the 81st minute.
Rossi played the ball into strike partner Nilmar on the edge of the box, and the Brazilian cleverly let the ball run across him to wrong-foot the visiting defence before thumping a shot past Mihailov.
At that stage Twente looked gone, but they gave themselves a slight lifeline in injury time when Janko headed in following good work by Wisgerhof, although Michel Preud'homme's side still have a massive task if they are to go through.
Villarreal 5-1 FC Twente: Match Report - view commentary, squad, and statictics of the game as it happened.