Celtic hold 10-man Atletico to get off Champions League mark
The Scottish champions struck after just four minutes through Kyogo Furuhashi before Antoine Griezmann levelled on the rebound after his penalty was turned onto the post by home goalkeeper Joe Hart.
Luis Palma restored Celtic's lead before half-time, but Alvaro Morata's header ensured Atletico's unbeaten run stretches to eight games.
The Spanish giants had Rodrigo De Paul sent off in the closing stages.
Celtic, though, could not make the man advantage count in the final eight minutes plus stoppage time as their 10-year wait for a Champions League group-stage win at home goes on.
A draw takes Atletico to within a point of Group E leaders Feyenoord, who beat Lazio 3-1 on Wednesday.
Celtic remain bottom, three points adrift of the third-placed Italians.
There could also be further ramifications from the match for Celtic after fans defied a club plea by waving Palestine flags in a show of support to people in Gaza during the war between Israel and Palestinian militants Hamas.
A leading Celtic fans' group announced they would distribute flags outside the stadium.
In a statement before the match, Celtic asked for "banners, flags and symbols relating to the conflict and those countries involved in it are not displayed at Celtic Park at this time".
Once the action got underway, the home side were inspired by the hostile atmosphere.
Matt O'Riley's through ball sliced open the Atletico defence for Kyogo to dink home his seventh goal of the season.
But Brendan Rodgers' men have found the step up to Champions League level tougher defensively and a naive challenge from Greg Taylor on Nahuel Molina handed the visitors a glorious chance to equalise.
Hart tipped Griezmann's spot-kick onto the woodwork, but the ball bounced back kindly for the French international to roll into an empty net.
Celtic hit back within three minutes when Palma blasted into the far corner from Daizen Maeda's cross.
Atletico thought they had levelled again before half-time only for Axel Witsel's header to be ruled out for offside.
Diego Simeone's men did not have to wait long after the break to equalise when Morata stooped to divert a brilliant header high past Hart from Marcos Llorente's cross on 53 minutes.
Atletico then looked set to go on and win the game as Celtic paid for their first-half efforts by tiring in the second period.
But De Paul dived in on Paulo Bernardo to earn a second yellow card and at least give the hosts some breathing space in the closing stages, even if they failed to find a winner.