A late goal from substitute Lasse Schone gave Ajax a 2-2 draw against Celtic at the Amsterdam ArenA where Hoops left-back Emilio Izaguirre was sent off.
In an absorbing encounter, right-back Mikael Lustig headed the Parkhead men into an interval lead in the 42nd minute after Danish midfielder Viktor Fischer had cancelled out midfielder Nir Bitton's eighth minute opener.
Celtic looked assured after the break but when Izaguirre was dismissed in the 74th minute by referee Luca Banti for picking up his second yellow of the night with a foul on Anwar El Ghazi, the home side came storming back with Schone scoring a free-kick in the 84th minute and Ronny Deila's side hanging on for a point.
Deila, under pressure after losing the top spot at the top of the Ladbrokes Premiership with a defeat at Aberdeen at the weekend, and having exited the Champions League at the play-off stage, suffered a blow with the loss of Charlie Mulgrew to a thigh injury - Stuart Armstrong and Scott Allan were also out injured.
That meant a debut for Croatia Under-21 stopper Jozo Simunovic, signed recently from Dinamo Zagreb.
Izaguirre returned with midfielders James Forrest and Kris Commons coming into the starting line-up.
Ajax, top of the Eredivisie and unbeaten in five league games, had 22-year-old German forward Amin Younes making his first competitive start, joined in attack by captain Davy Klaassen and El Ghazi.
Celtic got off to a confidence-boosting start when Commons set up Bitton who had time and space to drill a right-footed shot from 16 yards low past Jasper Cillessen, giving the Ajax keeper no chance.
The Dutch side tried to quickly get back into the match, somewhat unconvincingly, but in the 25th minute they levelled with a well-worked goal.
The talented Younes went past Lustig with ease before slipping the ball to Klaassen, whose clever flick to Fischer was fired past the diving Hoops keeper Craig Gordon from the edge of the box.
The goal appeared to strip Deila's side of some confidence as Ajax, by contrast, started to move the ball around with more belief.
However, in the 39th minute Celtic could have got themselves back in front from a quick throw-in when Forrest raced along the bye-line before picking out Leigh Griffiths a few yards from goal.
The Hoops striker failed to connect properly with his shot although Cillessen still did well to push the ball past the post for a corner, which came to nothing.
But it was from a corner three minutes later that Lustig rose highest to head in Commons' deep cross, giving the Parkhead side the half-time advantage.
Celtic looked the more likely to get the next goal in the second-half, but the game changed when Izaguirre got his marching orders.
The Honduras international, booked just after the break for a challenge on Kenny Tete, was allowed a couple more fouls before referee Banti deemed his trip on El Ghazi to be one too many, leaving Celtic to replace Forrest with defender Tyler Blackett and fight with 10 men.
Ajax substitute Arkadiusz Milik, on for Younes, hit the post with a header in the 79th minute, after Klaassen had gone close, also with a header.
But Celtic were undone when Schone, on for Fischer in the 75th minute, fired in a free-kick from wide on the left which beat everyone including Gordon and ended up in the net.
Milik headed just over as Ajax threw everything forward looking for the winner but the Hoops held out four minutes off added time although they will look at Izaguirre's dismissal as the cause of a nervy ending.
Celtic manager Deila told BT Sport 2: "It's always tough away in Europe, especially here in Amsterdam.
"We showed very good work and attitude, we were very organised and I think we were unlucky to get the red card.
"Emilio played well to negate the situation. In the first half he didn't do anything wrong but in the second half (El Ghazi) gets more inside and we get into trouble.
"It was tough in the beginning (with 10 men), they got more crosses in, but when we got five behind we were very secure and didn't concede many chances."
Deila was satisfied with a point, though, and added: "I'm very proud, we have had a tough period, we have many games left but this is a good start.
"Confidence will come and we will get better and better."
CELTIC PLAYER RATINGS
Craig Gordon 6
Mikael Lustig 6
Dedryck Boyata 7
Jozo Simunovic 6
Emilio Izaguirre 5
Nir Bitton 7
Scott Brown 7
James Forrest 6
Stefan Johansen 6
Kris Commons 7
Leigh Griffiths 6
Substitutes:
Tyler Blackett: 5
Efe Ambrose: 5
Saidy Janko: 5
STAR PLAYER
Bitton scored a fine opener and showed class and composure on the ball. Rapidly turning into one of Celtic's most important players.
MOMENT OF THE MATCH
Ajax's first equaliser. Amin Younes went past Mikael Lustig with ease before slipping the ball to skipper Davy Klaassen, whose clever flick to Viktor Fischer was fired past the diving Hoops keeper Craig Gordon from the edge of the box.
VIEW FROM THE BENCH
Parkhead boss Ronny Deila believes Celtic would have won had Emilio Izaguirre not been sent off while Frank de Boer will have been glad with a point after trailing 2-1 in the second half and not really looking like drawing level until the dismissal.
MOAN OF THE MATCH
Izaguirre's sending off could easily have been avoided. He was let off with a couple of fouls before the referee could take no more. Should have been more disciplined.
TWEET OF THE MATCH
"#Celtic discipline and defending set pieces cost us the 3 points. I'll take the draw, but could have been sweeter." - Celtic fan and '24: Live Another Day' actor Ross McCall.
https://twitter.com/maccageezer/status/644584846182891520
