The hosts raced into a 2-0 lead with goals from Carlos Mane and the classy Iuri Medeiros before Celtic's Lewis Kidd scored a 20-yard strike on the stroke of half-time to keep the Scots in the game at the break.
Despite all their second half efforts, Celtic could not find an equaliser and remain rooted to the bottom of the group but still have a chance at proceeding through to the last 16 should they beat PSV away next week.
Barcelona qualified for the last 16 with a 3-1 win against Wolfsburg at the Mini Estadi.
Goals from Adama Traore, Sandro Ramirez and Ebswelle saw the Catalans ease past their German opponents, playing some exceptional football in the process.
The visitors grabbed a consolation goal on 89 minutes, but rarely threatened and the hosts were well worth the three points.
Barca will win Group One if Tottenham fail to beat Anderlecht by four goals in their final fixture in December.
Elsewhere, Rosenborg extended their lead at the top of Group Five with a 2-2 draw against Borussia Dortmund.
The Norwegians got off to a flying start with Robin Bjornholm rounding the keeper to take the visitors into a 1-0 lead after just 60 seconds.
Dortmund struck back 20 minutes later through Said Benkarit who exquisitely chipped the ball over Stroevik from the edge of the area, to draw the sides level.
Just before the break Magnus Blakstad flicked on from a well worked free-kick to take the visitors into a 2-1 lead.
The Germans came out for the second-half looking far more fluid in midfield and created plenty of chances.
The equaliser eventually came on 66 minutes through Domink Beutler, to ensure Dortmund remain in the hunt for a last-16 place.