Villarreal captain Marcos Senna's brilliant free-kick consigned Celtic to yet another defeat on their Champions League travels.
The Hoops had taken one point from a possible 45 away from Parkhead in this stage of the competition before their second Group E game of this campaign. Make that one from 48 now.
Celtic striker Georgios Samaras squandered a great chance just before the interval when he fired straight at Diego Lopez.
And the visitors were made to pay for that miss after Paul Hartley fouled Joseba Llorente 25 yards from goal as Senna curled the ball past Artur Boruc who had yet another busy evening.
Celtic manager Gordon Strachan's bold line-up, packed with attack-minded players, promised a more open game than perhaps the Scots had indulged in during their recent barren seasons away in Europe.
But when the final whistle sounded, after 90 minutes of mostly chasing a slick-moving Spanish side, their future in this season's competition was left in tatters.
After drawing 0-0 with Danish side Aalborg in their first game, they will need to find something special if they are to get past Manchester United or Villarreal to reach the last 16 for the third season in succession.
It was a long night for Celtic. Joseba Llorente fired a volley just over the bar within two minutes to hint at the potency of the Spanish side.
Then, in the 14th minute, with Celtic looking relatively comfortable, Villarreal midfielder Sebastian Eguren headed Rossi's cross well past the post from 10 yards when it seemed easier to beat Boruc.
Villarreal slowly began to build momentum and, following a defense-splitting Eguren pass, Boruc, after a second of consideration, had to rush from his goals to block Giuseppe Rossi.
When the ball rebounded outside the box, Llorente, under no pressure, carelessly curled it wide of the target.
Then Llorente headed Senna's corner straight into the arms of Boruc from barely 12 yards out.
The Scottish champions responded and during a brief moment of respite Aiden McGeady flashed a 25-yard drive two yards wide.
The Celtic defense was not under siege but, inspired by former Arsenal midfielder Robert Pires who floated around the midfield, the home side were undoubtedly in control.
In the 35th minute Boruc appeared to tip over a clipped shot from Rossi following good play by Santi Cazorla but referee Viktor Kassai gave a goal kick.
Three minutes from the break, Celtic passed up on the best chance of the half.
Samaras broke free of the Villarreal defense to race on to a Mark Wilson pass and take advantage of a mistake by Villarreal defender Diego Godin but the former Manchester City striker was too casual with his shot from 14 yards, allowing Diego Lopez to block.
Celtic survived a late surge of pressure but the home side appeared to be quickly into their stride after the break.
However, the Glasgow side won their first corner of the second half in the 48th minute and from Shunsuke Nakamura's cross, Gary Caldwell's header towards goal was helped on its way by captain Stephen McManus but the ball landed fortuitously in the arms of Diego Lopez.
Villarreal raced up the pitch moments later and after Rossi had twisted and turned as he drove towards the Celtic box, he drilled his shot inches wide of Boruc's left-hand post.
Still the Spanish side dominated but there was enough evidence in Celtic's occasional breaks to suggest that elusive away win in Europe was not out of their reach.
On the hour mark, as Villarreal again swarmed around the Parkhead side's penalty area, Santi Cazorla tested Boruc with a long-range drive, the Celtic 'keeper clutching the ball safely to his chest before making an even better block moments later from Senna's powerful 30-yard effort.
But in the 67th minute, after Hartley had fouled Llorente 25 yards from goal, Senna curled the free-kick superbly past Boruc and El Madrigal erupted.
The goal clearly deflated Celtic and manager Strachan threw on Scott McDonald for Shaun Maloney and Barry Robson for Nakamura to try to salvage something.
The equalizer almost arrived in the 75th minute when Australian international McDonald sent a wonderful dipping volley from inside the box just over the bar.
Jan Vennegoor of Hesselink replaced Hartley as Celtic went for broke.
But as Celtic left gaps, Boruc had to save again from Llorente after McManus had blocked his first effort with his body.
Boruc had another fine save in the 89th minute, this time from Santi Cazorla's drive which was heading for the bottom corner, leaving the scoreline respectable but ultimately bringing Celtic no reward.
