The visitors started brightly with Goerges Mikautadze taking advantage of an erroneous header from Reds captain Virgil van Dijk to give his side a 1-0 lead.
Villarreal doubled their lead at the half hour mark with Sergi Cardona finishing off a swift counter attacking move following a great pass from Nathan Saliba.
Argentina midfielder Alexis Mac Allister pulled one back for the home side six minutes later, with a neat header following a Kostas Tsimikas corner kick.
Liverpool drew level at the stroke of half time after Ronald Araujo latched onto a Rio Ngumoha curling cross to head home from the far post.
The Reds threatened from the start of the second half with Cody Gakpo and Trey Nyoni coming close to scoring before Ngumoha set up Mac Allister for a simple 66th minute tap in to take a 3-2 lead.
German attacker Florian Wirtz added a fourth just three minutes later after a flowing attacking move and assist from Dutch star Gakpo.
The Yellow Submarine tried to fight back and eventually found a third goal through Tani Oluwaseyi finish in the 87th minute but Liverpool held on to claim their third successive victory in the competition this season.
"It definitely hasn't been a boring game," said Liverpool manager Andoni Iraola.
"I think they've been much better than us, especially the first 30-35 minutes until the 2-0. We did much better than them in the second half, especially the 30-35 minutes until the fourth goal, probably.
"We've probably started too relaxed in the game and even at the end, the 4-2. You think it's done, and they keep you there until the end, because they are a very good team.
"I value the three points a lot because we were facing a really good team today. I knew because I know them very well and I know how good they are and that’s the reason why I give importance and value to this win."
The Reds are scheduled to face Turkish giants Fenerbahce in their next UEFA Champions League fixture early next month.
Enzo Maresca has made it his mission to help Phil Foden rediscover his best form and re-establish himself as one of England's leading players after the Manchester City midfielder ended his goal drought in spectacular fashion.
Vincent Kompany has played down fears of serious injuries to Luis Diaz and Min-jae Kim after Bayern Munich's 2-2 draw with Arsenal in the Champions League on Wednesday.
Jose Mourinho has praised Real Madrid's squad depth after their 4-1 Champions League win over RB Leipzig but insisted his team must improve before Sunday's El Clásico against FC Barcelona.
Virgil van Dijk believes Rio Ngumoha has a bright future at Liverpool after the teenage winger played a key role in their thrilling 4-3 Champions League victory over Villarreal at Anfield.
