The slick-passing visitors proved more than a match for Neil Lennon's men although the Hoops had their chances.
However, in a frustrating night in the east end of Glasgow, Sion's inspired number one had good saves from Charlie Mulgrew, Kris Commons and substitute Shaun Maloney to keep the tie in the balance ahead of the second leg next week in Switzerland next week.
The Parkhead club will certainly have to improve if they are not to find themselves out of Europe again so early in the season, but Sion showed enough to promise a tasty return game.
Lennon, who raged for most of the night at the touchline, was dealt a blow when stopper Kelvin Wilson had to drop out with a leg injury.
Mulgrew came inside to partner Daniel Majstorovic in the heart of the Hoops defence with Mark Wilson moving to left-back and Cha Du-ri in at right-back for his first appearance of the season.
Goalkeeper Fraser Forster, signed last night on another season-long loan deal from Newcastle, made his second debut in place of Lukasz Zaluska, who dropped to the bench as striker Georgios Samaras replaced Gary Hooper, who injured his ankle against Dundee United at the weekend.
The match was surrounded by some intrigue as Sion had travelled to Glasgow with five players who, in the eyes of FIFA, were ineligible.
The Swiss club had allegedly broken a signing embargo to recruit the players and two of them, Pascal Feindouno and former Hearts defender Jose Goncalves, were in the starting line-up.
Sion started with two men in attack - unusual for a visiting team to Parkhead - and they had contained the inevitable whirlwind start by Celtic with some ease and began to grow into the game.
Lennon's men were being asked questions not posed on a weekly basis in Scotland as they scurried around trying to get their fair share of possession.
Gradually Celtic stepped up the pressure. Vanins spilled Mulgrew's cut-back to cause some panic in the visiting defence but Samaras' back-heel from 10 yards was blocked by sheer numbers.
In the 33rd minute, after Sion stopper Michael Dingsdag had been booked for fouling Commons 25 yards out, Mulgrew flighted in a curling free-kick which Vanins tipped over for a corner that eventually came to nothing.
Three minutes later, to add to the sense of frustration swirling around the stadium, Celtic striker Anthony Stokes was booked by Croatian referee Marijo Strahonja for diving in the box as he went past Vanins.
In the final seconds of the first half Commons had a close-range header saved by the Sion goalkeeper after climbing high at the back post to reach a Cha cross.
Wilson swapped positions with Mulgrew for the start of the second half which Commons began with a drive from distance that flew high over the bar.
Moments later, Samaras was equally lofty with his half-volley from 14 yards from another Cha cross.
James Forrest replaced Commons after 56 minutes as Lennon changed tact again but with Feinduono lively and Giovanni Sio a threat with his pace, the game remained finely balanced.
In the 68th minute Maloney replaced Stokes to some jeers from the home fans, wondering perhaps how Samaras had avoided the hook.
Two minutes later, though, Maloney was brought down 25 yards from goal by Jose Adailton and his free-kick had Vanins diving down to his right-hand post to keep the ball out and Samaras' attempt from the rebound.
Forster then had to tip a Sio free-kick from distance over the bar but flapped at the resultant corner and was lucky to see the ball end up in his hands.
At the other end, Vanins made his first mistake of the night when he punched a Mulgrew cross straight to Scott Brown but the Celtic skipper missed the target with his returned shot.
With his last throw of the dice Lennon sent on fans' favourite Paddy McCourt for Samaras to huge cheers, but it was Ki Sung-yueng who tested Vanins next with a low drive which the goalkeeper blocked.
The Hoops players trooped off to the sound of boos from their own supporters, who will view next week's game with some trepidation.