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.
Aden McCarthy netted his maiden goal in the UEFA Champions League but it was not enough for his team Sabah as they fell to a 2-1 home defeat against Borussia Dortmund in Baku.
Liverpool boss Andoni Iraola has revealed that Villarreal counterpart Inigo Perez was his preferred choice to join his coaching staff before a work permit rejection prevented the Spaniard from moving to Bournemouth in 2023.
Marc Guehi believes Manchester City can continue to develop under Enzo Maresca as they prepare to face AEK Athens in the UEFA Champions League on Tuesday.
Barcelona midfielder Pedri has jokingly warned his close friend Ferran Torres not to score when the Catalan side face Paris Saint-Germain in a major Champions League clash tonight at Parc des Princes.
