- Kyogo Furuhashi (4')
- Luis Palma (28')
- Antoine Griezmann (25')
- Álvaro Morata (53')
- Rodrigo De Paul (82')
Feyenoord took over top spot in the standings on six points after a 3-1 win at Lazio earlier on Wednesday and the draw left Atletico second on five points, one clear of Italy's Lazio in third. Celtic are bottom with one point from three games.
Roared on at a sold-out Celtic Park, speedy Kyogo Furuhashi made the most of the hosts' early pressure and ghosted between two Atletico defenders to open the scoring with a tidy close-range finish after four minutes.
Atletico equalised when Antoine Griezmann put the ball into an empty net after his penalty had struck the post.
Luis Palma put Celtic back ahead three minutes later with a brilliant curling shot from a wide angle.
Atletico equalised again, however, in the 53rd minute with fine diving header by Alvaro Morata that arched over goalkeeper Joe Hart.
The visitors dominated the closing stages and missed several chances to grab a winner before midfielder Rodrigo de Paul was shown a second yellow card for a hint of contact in a challenge with Paulo Bernardo, but the Spanish side hung on the draw.
"We were able to turn the game around as it was going. In the second half we were dominating, but the red card for De Paul, which is dubious, hurts. With 11 men it would have been different, but at least we leave with a point," Atletico defender Mario Hermoso told Movistar Plus.
"The team was pushing and they were already looking tired at the back, we could see it. These are things that happen in football and we hope to do well when we see them at our home."
- Felix Zwayer