Match ends, Molde 3, Celtic 1.
Celtic's chances of a place in the knockout phase of the Europa League were reduced as Molde consolidated their lead at the top of Group A.
In atrocious conditions, Dedryck Boyata's slack pass paved the way for Ola Kamara to secure an early lead.
That was followed by a second from Vegard Forren on 18 minutes, which put the Norwegian champions in command.
Kris Commons reduced the deficit after the break, but Mohamed Elyounoussi soon restored the two-goal advantage.
It means Celtic trail Molde by five points before their return match at Celtic Park in two weeks' time.
They and Ajax sit on two points, two behind Fenerbahce following the Turks' 1-0 victory over the Dutch in Istanbul.
Celtic have been undone by slack defensive play and questionable goalkeeping on more than one occasion this season and both were in evidence again.
Boyata gifted possession to Elyounoussi for the first goal and Craig Gordon looked cumbersome as he tried to keep out Kamara's near-post shot.
Molde centre-half Joona Toivio was allowed to cross for his defensive partner Forren to volley unchallenged past Gordon for the second.
And it was too easy for Molde to open up the visitors' defence for a third when Celtic should have been revitalised having just got back into the game.
Molde could have added more in the second half as Kamara - Deila's former protege at Stromsgodset - twice passed up excellent opportunities and Gordon saved well from Etzaz Hussain.
Nir Bitton almost made the scoreline more respectable with a late shot off the bar, but that would have been an unfair reflection of Molde's dominance.
An unhappy homecoming
Ronny Deila had played down the significance of his own return to Norway, stressing merely his constant desire to win football matches.
Yet it was Ole Gunnar Solskjaer who was able to celebrate a winning return to Norwegian football.
The reappointed Molde head coach - a local hero already in these parts - may not have been back in charge long enough to take great credit for any tactical masterstrokes, but his side outfought and out-thought Celtic.
After a tentative start, they bossed the game and have given themselves an excellent chance of progressing in the competition.
There was tension in the visiting ranks as Commons was taken off despite being one of the few Celtic players to offer a threat.
The forward directed his anger at the Celtic bench as the supporters sang his name.
It is one of a number of issues that need to be addressed if Celtic are to turn this European campaign around.
Stats you need to know
- The Bhoys have kept one clean sheet in their last 18 Europa League games, conceding 32 goals in a run stretching back to December 2009.
- Celtic have now let in two or more goals in each of their last five European games (including qualifiers).
- There were 47 seconds between Commons' goal for Celtic and Elyounoussi's for Molde.
- 23RindaroySubstituted forFloat 52'minutes
- 11KamaraSubstituted forHestadat 74'minutes
- 24ElyounoussiSubstituted forBakengaat 84'minutes
- 2Semb Berge
- 34da Silva
- 4AmbroseBooked at 82mins
- 15CommonsSubstituted forCiftciat 76'minutes
- 14ArmstrongSubstituted forMackay-Stevenat 74'minutes
- Vladislav Bezborodov
- Shots on Target
Second Half ends, Molde 3, Celtic 1.
Mikael Lustig (Celtic) wins a free kick on the right wing.
Foul by Eirik Hestad (Molde).
Attempt missed. Nir Bitton (Celtic) left footed shot from outside the box is high and wide to the left. Assisted by Gary Mackay-Steven.
Nir Bitton (Celtic) wins a free kick in the attacking half.
Foul by Mushaga Bakenga (Molde).
Attempt saved. Nir Bitton (Celtic) right footed shot from outside the box is saved in the centre of the goal.
Attempt missed. Nadir Ciftci (Celtic) header from the centre of the box misses to the left. Assisted by Mikael Lustig with a cross.
Dedryck Boyata (Celtic) wins a free kick in the defensive half.
Foul by Mushaga Bakenga (Molde).
Nir Bitton (Celtic) hits the bar with a right footed shot from outside the box.
Attempt missed. Per Egil Flo (Molde) right footed shot from the right side of the box misses to the left. Assisted by Eirik Hestad with a cross following a corner.
Substitution, Molde. Mushaga Bakenga replaces Mohammed Elyounoussi.
Corner, Molde. Conceded by Craig Gordon.
Attempt saved. Etzaz Hussain (Molde) left footed shot from the centre of the box is saved in the centre of the goal. Assisted by Mohammed Elyounoussi.
Attempt missed. Vegard Forren (Molde) header from the centre of the box misses to the left. Assisted by Joona Toivio with a cross following a set piece situation.
Efe Ambrose (Celtic) is shown the yellow card for a bad foul.
Foul by Efe Ambrose (Celtic).
Martin Linnes (Molde) wins a free kick on the right wing.