VILLARREAL, Spain -- Liverpool march on in their pursuit of the Quadruple. Though they can now prepare for a 10th Champions League final later this month, against either Manchester City or Real Madrid in Paris, it required another display of the club's incredible resilience in European competition on Tuesday to seal a 3-2 win against Villarreal at Estadio de la Ceramica.

Jurgen Klopp's squad were so poor in the first half -- outrun, out-tackled and out-thought by their Spanish opponents -- that goals by Boulaye Dia and Francis Coquelin had given Villarreal a 2-0 lead which cancelled out Liverpool's two-goal advantage from last week's first-leg. Liverpool's three touches in Villarreal's box before the half was their lowest in a first half all season in all competitions.

Had referee Danny Makkelie awarded the home side a penalty on 37 minutes -- four minutes before Coquelin's headed goal -- after goalkeeper Alisson Becker appeared to bring down Giovani Lo Celso, Liverpool could have gone in trailing 3-0 at halftime, their season threatening to implode in front of a blizzard of 23,000 yellow flags.

But Klopp's decision to replace Diogo Jota with Luis Diaz at the break turned the game in Liverpool's favour as the Colombian winger transformed his team's approach from submission to aggressive ambition.

Diaz ran at Villarreal, defused their first-half tempo and allowed Liverpool to gain control of the game. By the time Villarreal keeper Geronimo Rulli gave Klopp's side a helping hand with a series of costly errors, Diaz had switched the momentum and made it an inevitability that Liverpool would reach a third Champions League final in five seasons.

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"Coming back like we came back in the second-half was really special," Klopp said. "Luis (Diaz) had a massive impact -- Diogo Jota wasn't the problem in the first half, we had 11 problems. We just needed to mix it up a bit. I wanted the players to be mentality monsters from the first minute, but Villarreal took all the risks in the first half and we had a football problem to solve.

"We have reached a final, but three of the competitions aren't finished yet. The finals show up in our schedule and we need to be ready for them, but it's going to be difficult."

While the record books will show that Liverpool made it to Paris with a 5-2 aggregate victory, progression to the final was anything but certain at half time in Villarreal's tiny stadium.

Liverpool completed the so-called "Miracle of Istanbul" by fighting back from 3-0 down against AC Milan to win the 2005 Champions League final, and they overturned a 3-0 first-leg deficit with a 4-0 Anfield victory against Barcelona in the 2019 semifinal, so a second-half comeback against last season's Europa League winners has some way to go to match their previous epic glory nights.

But this victory and performance will enter Liverpool folklore because it provided evidence of the qualities that are often overlooked because of the world-class quality of Klopp's team.

To achieve great things, all athletes or teams must overcome some kind of adversity along the way, and this was undoubtedly a test of Liverpool's resolve and fighting spirit.

Liverpool were rocking badly in the first half. Villarreal coach Unai Emery had sent his team out with a game plan to press Liverpool incessantly and heap pressure on their defence. In midfield, Etienne Capoue (sent off for a second booking on 85 minutes), Dani Parejo and Francis Coquelin were outstanding, while Lo Celso found space to carve holes in Liverpool's defence.

Up front, Gerard Moreno and Dia tormented Virgil van Dijk and Ibrahima Konate. Villarreal also profited from gaps down the Liverpool right, where both Mohamed Salah and Trent Alexander-Arnold failed to do their defensive duties. Dia's third-minute opener from Capoue's lay-off gave Emery's team the belief they could hurt Liverpool and they dominated the play, with Coquelin making it 2-0 on 41 minutes.

It led to arguably Klopp's most important halftime of the season, and he went on the front foot by introducing Diaz, who has been a sensation since his £50m signing from Porto in January.

With Diaz darting down the left, Liverpool began to gain possession and create chances, and they regained the overall lead in the tie when Fabinho shot through Rulli's legs on 62 minutes.

Five minutes later, Diaz headed in an Alexander-Arnold cross to make it 2-2 on the night and 4-2 on aggregate before Sadio Mane completed the scoring on 74 minutes after Rulli had raced out of his area and missed the ball badly.

From being on course to be knocked out, Liverpool had turned the tie around inside half an hour and it was simply because of the manager's boldness and the team's ability to click into a higher gear.

Only the best teams can do that so quickly and with such devastating effect -- and Liverpool are in that bracket. But so are Manchester City and Real Madrid, who meet in Madrid on Wednesday to decide who will face Liverpool on May 28.

Real have had their unforgettable fightbacks this season, against Paris Saint-Germain and Chelsea, but City have yet to be tested in such a way. If it comes down to Liverpool facing City in Paris, however, there will be no question marks over the mentality of Klopp and his players -- and the opposition will know that too.

That's why this win in Villarreal was so important. It sent a message to the rest that Liverpool never know when they are beaten and they could end up with four trophies this season because of it.

No English team has ever won the Quadruple -- the FA Cup, the Carabao Cup, the UEFA Champions League and the English Premier League -- in a season, but Liverpool moved one step closer in convincing fashion.