Ademola Lookman gave La Dea an early lead to make Juve fans feel even worse following their recent points deduction, before Angel Di Maria equalised from the penalty spot and Arkadiusz Milik put the Bianconeri ahead with a stunning finish.
After the break, the Bergamaschi made a comeback of their own with goals from Joakim Maehle and a second one from Lookman, but Danilo levelled the score for La Vecchia Signora with a free-kick.
Juventus overcome early Lookman goal
Atalanta took the lead after just five minutes when Jeremie Boga found Lookman to his right, and the Orobici winger beat Wojciech Szczesny with a shot at the near post that the Juventus goalkeeper was not able to keep out.
After that goal, Di Maria had a shot easily saved by La Dea goalkeeper Juan Musso, and he took the opportunity to equalise for the Bianconeri after a VAR review. Atalanta defender Giorgio Scalvini had fouled Manuel Locatelli in the area and the Argentinian veteran sent his spot kick into the bottom right corner in the 26th minute.
The comeback was complete 10 minutes before half-time when a Di Maria back-heel sent Nicolo Fagioli down the right wing, and his cross found Milik, who beat Musso with a superb half-volley.
Atalanta fly out the blocks
It took just 35 seconds into the second half for Atalanta to draw level, with Scalvini winning the ball on the left flank and passing to Lookman, who then played the ball to Maehle, and the Dane beat Szczesny with a low shot. La Dea regained the lead after 53 minutes when some excellent wing play from Boga found Lookman, whose header gave Szczesny little hope of saving it.
In the 65th minute, Locatelli earned a free-kick that Di Maria took and he laid the ball off for Danilo to smash low into the net. Rafael Toloi nearly regained the lead for the Bergamaschi, but Szczesny was able to push the ball away, while Juve sub Fabio Miretti had a header that was easy for Musso to save.
Juventus remain midtable, Atalanta squander chance to earn top-four spot
This result will feel like two points lost for both sides. Juventus go up to ninth on 23 points and they are five points way from getting a Conference League spot.
Meanwhile, Atalanta are fifth with 35 points, but a victory would have put them level with Inter and AS Roma, and put them in a position to earn a Champions League place for 2023/24.