Nuno Espirito Santo's side go into next Thursday's last-32 second-leg in Barcelona firmly in the driving seat after completely outclassing La Liga's bottom club.
Jota got the ball rolling with a close-range effort in the first half.
An outrageous volley from compatriot Neves made it two, and then Jota wrapped up a terrific treble with two more sharp finishes.
Barring a miraculous turnaround at the RCDE Stadium, Wolves' European journey will continue.
Watched by a packed-out Molineux, including Fosun chairman Guo Guangchang, Wolves were the firm favourites.
The fact Espanyol had made nine changes to the side which drew 2-2 with Sevilla in the league last weekend added to the expectation, too.
And, blimey, did Nuno's charges live up to their billing.
Wolves – Jota and Neves in particular – were far too hot to handle for the Spanish outfit.
Neves's goal was out of this world, and on any other night would have grabbed the headlines.
But it was Jota who really took the game by the scruff of the neck, getting back amongst the goals and tearing Espanyol apart.
Two special players stepping up to the plate, while the rest of the Wolves team did their jobs to an excellent standard.
The visitors were not the greatest, it must be said, but on this evidence, Nuno & Co could well go all the way in this competition.
Wolves made two changes to the side which drew 0-0 with Leicester last Friday, with Joao Moutinho and Adama Traore returning to the starting line-up.
Leander Dendoncker and Pedro Neto dropped to an attacking bench, which also included January signings Daniel Podence and Leonardo Campana – but not Morgan Gibbs-White.
Espanyol, meanwhile, had Chinese star Wu Lei playing in a much-changed XI.
Double-headers are never won in the first leg, of course, but a healthy margin to take into the second meeting goes a long way.
And Wolves' intentions were clear – get the ball forward and look to break the deadlock early on.
Moutinho and Neves both tried their luck from distance in the first few minutes, and while those efforts went wayward, they were a sign of what was to come.
Nuno's men opened the scoring with their next attempt, a quarter of an hour into the encounter.
Sharp work from Traore saw him earn Wolves a corner, and, from that, the visitors were punished.
Moutinho's outswinger was flicked on by Raul Jimenez to Jota, who adjusted quickly and finished on the volley via a Victor Sanchez deflection.
The first time Wolves have scored first in a match since the 4-0 Europa group stage triumph against Besiktas on December 12 – Jota the man on the mark then, as well. The Portuguese's first goal since that success, too.
It was exactly the start the hosts were searching for, but they were lucky to still be in front at the interval.
Rui Patricio, bizarrely, attempted to volley a looping ball but completely missed it.
Facundo Ferreyra only had to poke the ball home from a few yards out, but he fluffed his lines and Patricio, somehow, was able to make the save and breathe a huge sigh of relief.
Espanyol were then fortunate not to have a man sent off. Ander Iturraspe decided to square up to Jota and force his head into the Portuguese after pushing him.
A yellow card was awarded, and, surprisingly, it was stuck to after a VAR review – the technology coming into effect for the competition's knockout stages.
It was not the most malicious incident you will ever see, but it was petulant, and similar instances have been met with a red plenty of times in the past.
At the beginning of the second period, Espanyol threatened. Wu Lei, who had also tested Patricio in the first half, had a free header from near the penalty spot sail inches wide of the post.
Then, just as Wolves began to need a moment of magic to ease the nerves, Neves entered the spotlight.
In similar style to his scorcher against Derby in the Championship a couple of years ago, the midfield maestro chested the ball down and unleashed a rasper past an utterly helpless Andres Prieto, sending the South Bank into delirium.
A true artist at work, coming up with another masterpiece and leaving Espanyol flabbergasted.
And, not content with a two-goal advantage to take to Catalonia, Jota came up with his second and Wolves' third of the night.
Found by the advancing Matt Doherty, Jota held off his marker, Victor Gomez, and found the net in fine fashion.
It took a slight nick off Gomez, but the Wolves man will not care one bit.
Astonishingly, he was not done there either. The Portuguese still had time to grab his hat-trick, and ninth goal in the competition.
He saved the best until last, too, ending a confident run by slamming the ball in from the edge of the area.
Jota, rightfully, received a standing ovation as he was replaced by Podence towards the end, on a night where Wolves blew Espanyol away. A first leg that could not have gone any better.
15 - GOOOOOOALLLLL! Just what the doctor ordered, Wolves are ahead! A corner comes in from Moutinho, and Jimenez flicks it on to Jota, who finishes via a deflection off Sanchez. Deadlock broken.
52 - GOOOOOOOOOOALLLLLLL WOOOWWWWW!!! Remember Derby? It's pretty much happened again! Neves chests the ball down and unleashes an exceptional volley past Prieto, making it 2-0 to Wolves. Sheer excellence.
67 - GOOOOOOAAALLLLLLL!!! It is 3-0 to Wolves! Jota holds off his marker and finishes past Prieto via another slight deflection, this time off Gomez, but it is his goal and Nuno's lot are in dreamland.
81 - GOOOOOALLLLLLLLLLLLL HAT-TRICK!!! Unbelievable. No deflection with this one, Jota goes on a marauding run and then rifles the ball into the net from the edge of the box. What a night for him, and Wolves!
Wolves (3-4-3): Patricio; Boly, Coady (c), Saiss; Doherty, Moutinho, Neves, Otto; Traore (Dendoncker, 60), Jimenez (Neto, 75), Jota (Podence, 83)
Subs not used: Ruddy (gk), Kilman, Jordao, Campana
Goals: Jota (15, 67, 81), Neves (52)
Espanyol (4-4-2): Prieto; Gomez (Darder, 75), Naldo, Calero, Didac; Melendo (Calleri, 60), Iturraspe (David Lopez, 60), Sanchez (c), Vargas; Ferreyra, Wu Lei
Subs not used: Diego Lopez (gk), Cabrera, Pedrosa, Embarba
Referee: Tobias Stieler (Germany)