Henrik Larsson saved Celtic's unbeaten home record at Parkhead but Josico's first-half goal put Villarreal in control of the UEFA Cup quarter-final.
Martin O'Neill drafted influential midfield duo Stilian Petrov and Neil Lennon back into his side for the game.
Lennon missed Saturday's dramatic 2-2 draw with Hearts through injury while Petrov came off the bench, but they returned to the starting 11 in place of Paul Lambert and Stephen McManus.
David Marshall continued in goal after his heroics in the Nou Camp in the last round, despite Robert Douglas recovering from a hip injury to take his place on the bench.
The La Liga side are on a high after sending Roma packing in the last round and drawing with Barcelona in the Catalan capital at the weekend.
Caretaker coach Francisco Garcia was without the suspended Juliano Belletti but he had Brazilian dangerman Sonny Anderson and Spanish international Jose Mari in attack.
Celtic, for whom Alan Thompson and Chris Sutton signed new deals on Wednesday, almost carved out a chance after 40 seconds.
Stanislav Varga lifted the ball over the top of the Villarreal defence and although Henrik Larsson got behind them he took his eye off the ball and Jose Reina gathered.
The noise inside Parkhead swept Celtic forward and Thompson curled a left-foot effort over the crossbar, from the edge of the box, after Fabricio Coloccini had
clattered the Swede.
But the Spanish side weathered the early storm and did what Hearts did at the weekend by snatching the opener following a contentious decision.
Referee Kyros Vassaras waved play on after Sebastian Battaglia seemed to foul Stilian Petrov just outside the area in the ninth minute.
But Villarreal swept down the opposite end to go ahead when Garcia Roger crossed from the left flank and Josico's glancing header flew into the corner of the net.
The visitors continued to look dangerous on the break and Juan Riquelme headed wide after Rodolfo Arruabarrena's deep cross had gone over the head of Varga.
Villarreal went close again in the 15th minute when Anderson fired just past the upright from just outside the box.
Petrov was given the perfect opportunity to cancel out that earlier decision and grab the equaliser in the 20th minute.
Sutton crossed from the left of the box but the Bulgarian skipper headed over from just six yards out.
The referee incensed the Celtic crowd again on the half-hour when he booked Pearson when Josico went down theatrically from his challenge.
Petrov again went close a minute later as Reina touched his volley, from Sutton's cross, behind off the upright but Vassaras and his assistant never saw it and awarded a goal-kick.
Josico took retribution against Pearson and was booked for a foul in the 36th minute before Villarreal squandered a glorious chance to stretch their lead.
The Celtic defence were caught out as Mari found himself clean through on goal but he blasted high over the top from 22 yards.
Larsson and Sutton combined in the dying seconds of the half to give the Englishman a sight on goal but his shot was saved low by Reina.
HT: Celtic 0 Villarreal 1
Celtic found themselves under more pressure immediately after the break but Larsson should have pulled his side back on level terms in the 48th minute.
Thompson's chip into the box fell kindly for the Swede but he failed to get a shot away and Arruabarrena got back to make a timely challenge.
The referee continued to frustrate the home side with some strange decisions which had O'Neill throwing his arms about on the sideline.
But Riquelme presented Anderson with a glorious chance to put his side into an even stronger position in the 52nd minute.
He threaded the ball through a stretched Celtic defence but as in the Nou Camp, Marshall came off his line to save his team-mates.
Larsson thought he had grabbed the equaliser in the 55th minute but, as he wheeled away to celebrate with the fans, the linesman flagged for what appeared to be handball.
O'Neill was raging at this point and had to be spoken to by the referee after the fourth official had complained about the Northern Irishman's behaviour.
Moments later, Varga's appeals for a penalty were rejected after his header seemed to strike a Villarreal hand before Petrov fired wide.
But justice was done in the 63rd minute when Celtic grabbed a deserved leveller.
Pearson chipped the ball out to Agathe and he whipped an inviting cross into the box for Larsson to get ahead of Reina to head into the empty net from eight yards.
The pressure and noise inside the ground did not cool Villarreal's menace on the break and Anderson's shot was deflected wide.
The drama continued as Roger received a yellow card for bringing down Petrov before Larsson also went into the book.
The home side continued their assault on the Villarreal goal and Larsson should have put his side ahead in the 70th minute.
Sutton did well on the touchline to pull the back into his path but he fired over the top with Reina struggling to make up the ground in the goal.
O'Neill brought Liam Miller on for Pearson in the 78th minute and Thompson then needlessly put himself out of the return leg in Spain with a frustrated challenge on Mari.
Celtic did not let that bother them and would have been ahead but for three top-class saves by Reina from Agathe, Varga and Sutton late on.
There was more drama in the dying seconds as Reina pushed Larsson's free-kick away and Sutton was unable to turn in the rebound before the referee again blew his whistle.
Teams
Celtic Marshall, Agathe, Balde, Varga, McNamara, Petrov,
Lennon, Pearson (Miller 79), Thompson, Larsson, Sutton.
Subs Not Used: Douglas, Valgaeren, Lambert, Mjallby, Beattie,
Smith.
Booked: Pearson, Larsson, Thompson.
Goals: Larsson 64.
Villarreal Reina, Javi Venta, Ballesteros, Coloccini,
Arruabarrena, Josico (Marti 78), Riquelme, Roger, Battaglia,
Jose Mari, Anderson.
Subs Not Used: Lopez Vallejo, Victor, Quique Alvarez, Calleja,
Arzo, Verza.
Booked: Josico, Roger.
Goals: Josico 9.
Att: 58,493
Ref: Kyros Vassaras (Greece).