The visitors fell behind on the half-hour when Cha Du-ri produced a horror piece of play when he went to help Rennes goalkeeper Benoit Costil's harmless goalkick towards his own keeper, Fraser Forster, only to see the ball go past him and into the back of the net.
Early in the second half, the Hoops still look shocked by the own-goal but managed to fight back and grab a leveler just over 20 minutes from time when Joe Ledley rose above a packed penalty area to head home Charlie Mulgrew's free-kick.
Mulgrew was close with a 30-yard set-piece attempt not long after before Forster came up with a vital save in the 79th minute to deny the home side and give the traveling Glaswegians a crucial point which sees them remain on the bottom of Group I with two points, equal with Rennes, after Udinese defeated Atletico Madrid 2-0 to go three points clear on top.
Europa League Group I
Yellow cards:REN - nil CEL - nil