Match ends, Ajax 2, Celtic 2.
Celtic were denied a Europa League win as Ajax's Lasse Schone scored a late equaliser in a captivating match.
Nir Bitton and Mikael Lustig were on target for a Celtic side who fought with real passion and determination.
But a stunning strike from Viktor Fischer and a free-kick leveller from Schone provided the sucker punches.
Celtic head back to Glasgow with a hard-fought point on a night that also saw Emilio Izaguirre sent off for receiving two bookings.
Ronny Deila, who handed a debut to young Croatian centre-back Jozo Simunovic and gave Kris Commons a first European start of the season, can be content with the result and performance.
But it is Molde who end Thursday on top of Group A after the Norwegian side defeated Fenerbahce in Turkey.
Sloppy Ajax punished
Unsurprisingly, the home side started with confidence and they stroked the ball about with a swagger as Celtic were forced to chase and contain.
But the Dutch side were punished for dithering in possession when Israel midfielder Bitton gave Celtic a stunning, if somewhat surprising lead.
He burst on to a Commons through ball on the right-hand side and slotted low past Jasper Cillessen on the angle from 12 yards out.
The imposing Amsterdam ArenA fell into near silence apart from the small band of Celtic fans high in the corner.
Frank de Boer's young hosts tried to hit back immediately but despite sustained pressure, the Celtic back four stood firm until they were sliced open by a piece of footballing brilliance.
Young German Amin Younes played the ball inside to Davy Klaassen on the edge of the box, the captain back-heeled into the path of Fischer and the forward simply stroked the ball past Craig Gordon with pinpoint accuracy.
A real touch of total football but a body blow to a Celtic side who had started to believe they could take their lead into the break.
The visitors started to grow in confidence, though, and Leigh Griffiths's close-range effort was turned behind by Cillessen.
However, any disappointment at that missed chance was blown away when Lustig put Celtic back in front from the resulting Commons corner.
The Sweden defender rose unchallenged on the six-yard line and nodded down and into the back of the net.
Klassen had a golden opportunity to level shortly after the break but he opted to back-heel inside the box instead of putting his foot on the ball and taking a shot - the howls of derision from the home fans a reminder that he chose the wrong option.
As Ajax continued to spurn chances, Celtic started to press in search of a third and James Forrest watched his fierce effort inside the box blocked desperately by Cillessen.
Griffiths then smashed the side netting with a volley after a superb looping ball from the ever more impressive Commons.
Red card turning point
Deila's side were reduced to 10 men after 73 minutes when Izaguirre was shown a second yellow card for a rash tackle on Anwar El Ghazi.
The visitors were saved by the woodwork when Younes's replacement Arkadiusz Milik headed past Gordon and watched his effort smash off the left-hand post.
Everything was pointing to this being Celtic's night but Denmark midfielder Schone killed the dream from a set piece as time began to run out.
His right-footed free-kick from 30 yards out on the left looked like a cross but it eluded everyone and bounced past a helpless Gordon.
Man of the match
Kris Commons impressed on his return to the starting line-up, setting up both Celtic goals and creating several other opportunities.
The former Scotland international looked at home when playing just off the central striker and linked well with his midfield team-mates.
The stats you need to know
- Lasse Schone has scored in the last three meetings of Ajax and Celtic.
- Having lost only one goal in their opening four European fixtures this season, Celtic have now conceded six in their last three.
- Celtic opened last season's Europa League group campaign with a 2-2 draw away from home, against Salzburg, and eventually reached the last 32 of the competition.
- Like in Amsterdam, Ronny Deila's side also led twice in that 2-2 draw in Austria.
Celtic return to domestic action with a home Scottish Premiership meeting with Dundee on Sunday at 15:00 BST. Their next Group A opponents are Fenerbahce in Glasgow on 1 October.
- 7FischerSubstituted forSchöneat 75'minutes
- 8SinkgravenSubstituted forSereroat 62'minutesBooked at 89mins
- 21El Ghazi
- 11YounesSubstituted forMilikat 62'minutes
- 2van Rhijn
- 4van der Hoorn
- 23LustigBooked at 64minsSubstituted forAmbroseat 69'minutes
- 3IzaguirreBooked at 73mins
- 49ForrestSubstituted forBlackettat 75'minutes
- 25JohansenBooked at 67mins
- 15CommonsSubstituted forJankoat 83'minutes
- Luca Banti
- Shots on Target
Second Half ends, Ajax 2, Celtic 2.
Attempt blocked. Davy Klaassen (Ajax) right footed shot from outside the box is blocked. Assisted by Lasse Schöne.
Delay over. They are ready to continue.
Delay in match Nir Bitton (Celtic) because of an injury.
Attempt missed. Arkadiusz Milik (Ajax) header from the centre of the box is just a bit too high. Assisted by Mitchell Dijks with a cross.
Offside, Celtic. Scott Brown tries a through ball, but Leigh Griffiths is caught offside.
Thulani Serero (Ajax) is shown the yellow card for a bad foul.
Foul by Thulani Serero (Ajax).
Efe Ambrose (Celtic) wins a free kick in the defensive half.
Attempt missed. Nemanja Gudelj (Ajax) right footed shot from outside the box misses to the right.
Foul by Nemanja Gudelj (Ajax).
Nir Bitton (Celtic) wins a free kick in the defensive half.
Attempt blocked. Thulani Serero (Ajax) right footed shot from outside the box is blocked.
Goal! Ajax 2, Celtic 2. Lasse Schöne (Ajax) from a free kick with a right footed shot to the bottom right corner.
Substitution, Celtic. Saidy Janko replaces Kris Commons.
Hand ball by Kris Commons (Celtic).
Davy Klaassen (Ajax) wins a free kick on the right wing.
Foul by Scott Brown (Celtic).
Arkadiusz Milik (Ajax) hits the left post with a header from the centre of the box. Assisted by Anwar El Ghazi with a cross.