Atalanta threw away the lead and risked losing in Berne, saved only by a Luis Muriel free kick and Juan Musso saves, so now must beat Villarreal to qualify for the Champions League knockouts.
La Dea knew Manchester United had beaten Villarreal 2-0 in the earlier kick-off, so a victory here would mean the Italians could reach the Round of 16 with just a point in their final home game against the Spaniards.
Robin Gosens, Hans Hateboer and Matteo Lovato were still out of action, but Young Boys had a huge injury list including Christian Fassnacht, goalkeeper David von Ballmoos, Mohamed Ali Camara, Cedric Zesiger, Jean-Pierre Nsame and Joel Monteiro.
The deadlock was broken within 10 minutes, as Remo Freuler pulled back from the left for Duvan Zapata, who gathered with his back to goal, spun round and the slight deflection gave the goalkeeper no chance from 12 yards.
Michel Aebischer drilled wide, while Jose Luis Palomino nodded a corner over from six yards, Mario Pasalic curled one off target and was tackled clean on goal by Sandro Lauper.
However, Young Boys equalised when an Aebischer corner found the glancing header of Jordan Siebatcheu at the near post, bouncing in off the underside of the crossbar.
Ruslan Malinovskyi’s trademark ferocious free kick stung the gloves of Guillame Faivre, but it was Palomino who restored Atalanta’s advantage with a splendid half-volley from the edge of the box on a cleared corner that flew into the far top corner.
Young Boys fought back, Juan Musso alert on Meschack Elia’s strike and rushing out on Fabian Rieder, while Felix Mambimbi’s effort was deflected over from a tricky angle.
However, Faivre made a fantastic fingertip save to deny Giuseppe Pezzella’s screamer on the volley. It proved crucial, as moments later Young Boys equalised when Atalanta were caught napping on a throw-in, knocked back from the by-line by Ngamaleu for Vincent Sierro’s strike.
La Dea visibly just switched off after the equaliser, an error almost gifting Siebatcheu a goal by sending him clear, then Silvan Hefti turning the game around with a well-placed curler into the far top corner from distance.
It still wasn’t over, as Luis Muriel came off the bench and scored with his first touch, a free kick from the edge of the box that surprised Faivre at the near post.
Musso had to make a desperate save in stoppages to prevent Lauper winning it for the Swiss outfit.
Young Boys 3-3 Atalanta
Duvan Zapata 10 (A), Siebatcheu 39 (Y), Palomino 51 (A), Sierro 80 (Y), Hefti 84 (Y), Muriel 88 (A)