Liverpool’s ambitions of reaching their first European final in almost a decade suffered a blow as Villarreal netted an injury-time winner in the first leg.
After a first half of few chances, Cedric Bakambu’s header clipped the Reds upright shortly after the break.
Liverpool went closest when Roberto Firmino’s low shot hit the post.
The Reds looked set for a creditable draw in Spain until they switched off to allow substitute Adrian Lopez to tap in Denis Suarez’s low cross.
Despite the dramatic winner, the Europa League semi-final still remains delicately poised before next Thursday’s return leg at Anfield.
The winners will face either Spanish holders Sevilla or Ukrainian side Shakhtar Donetsk, who drew 2-2 in their first leg, in the Swiss city of Basel on 18 May.
Liverpool have not reached a European final since losing to AC Milan in the 2007 Champions League showpiece, but a stoic display at La Liga’s fourth-placed team looked set to leave them a home win away from ending that barren run.
However, the Premier League side lost their defensive discipline in the final few seconds – and it could prove crucial.
Left-back Alberto Moreno wandered up field, leaving the space for former Manchester City youngster Suarez to exploit before squaring to Lopez for the easiest of finishes.
BBC Radio 5 live summariser and former Reds defender Mark Lawrenson said: “Where did the left-back disappear to? Injury time at 0-0 in a Europa League semi-final – and he’s probably 70 metres up the pitch.
“0-0 would have been a very good result. All of a sudden because of one aberration you’re under pressure for the second leg.”
Liverpool will have to score at least twice to go through in 90 minutes at Anfield, but Villarreal know an away goal would mean the Reds then need a minimum of three.
Reds lack attacking threat
Jurgen Klopp’s Liverpool side were installed as favourites to win Europe’s secondary club competition after their thrilling quarter-final win against Bundesliga club Borussia Dortmund.
Publicly the 48-year-old German insists there has been no thought about the possibility of reaching the final – but winning the trophy will cap an encouraging debut season with a place in next season’s Champions League.
His predecessor, Brendan Rodgers, named an inexperienced side in the Reds’ opening two matches in the competition, but Klopp has chosen stronger teams since arriving in early October.
However, he decided to play without a recognised striker at Villarreal, leaving England international Daniel Sturridge on the bench throughout – and the Reds offered little attacking threat.
Wales midfielder Joe Allen wasted the best chance in a tight first half, side-footing straight at home keeper Sergio Asenjo early on.
Further opportunities were rare, although Brazil forward Firmino – playing as Liverpool’s most advanced player – thumped an angled 12-yard drive against the base of the right post.
Liverpool were playing their first match since inquests concluded 96 Reds supporters who died as a result of a crush in the 1989 Hillsborough disaster were unlawfully killed.
Villarreal paid tribute to the victims by providing a banner – bearing the number 96 and Liverpool club slogan ‘You’ll Never Walk Alone’ – for their fans to hold up before kick-off.
“We were very saddened by the Hillsborough tragedy and we planned events to show the solidarity and support which our club and our fans have with Liverpool and those who were affected,” said the Spanish club.
‘This race is not over’
“Of course I’m not too happy with the goal we conceded in the last second. Counter-attacking in the 92nd minute makes not much sense – but it is only the first leg.
“It is 1-0 and they have to come to Anfield where we know how strong we are. We had our moments, we defended really good. This race is not over.
“If we had enough players around the box it was no problem but they played this one chip ball over Kolo [Toure], I don’t know where Alberto [Moreno] was in this moment but that was the only big mistake we made in this game and they scored with it.”
Villarreal manager Marcelino:
“Until the final whistle you can score or concede a goal and this time we were lucky enough to score in the very last minute.
“We managed a good result but we don’t know if it will be enough or not until the end of the tie.
“It was not an unfair result and we didn’t beat Liverpool by being lucky.”