Elsad Zverotic's stunning equaliser two minutes from time earned the Swiss side a shock draw to leave Liverpool needing a result against Udinese in their final group game to progress.
Joe Cole's effort looked to have secured the win for Liverpool after Raul Bobadilla had cancelled out Jonjo Shelvey's first-half opener, but Zverotic had the final word with a great strike to set up a nervy final round of games in Group A for Liverpool.
After Young Boys defender Dusan Veskovac was carried off with a hamstring injury, Jordan Henderson failed to take advantage of being put clean through by Shelvey's nifty backheel with Marco Wolfli saving at the expense of a corner.
Suso also had a shot saved before, on the half-hour, Brendan Rodgers was forced to send on Steven Gerrard for the apparently injured Andre Wisdom, meaning Henderson shuffled out to right-back.
Within two minutes Liverpool were ahead with Cole playing a significant part.
The former Chelsea midfielder exchanged passes with Suso, whose return was perfectly weighted to allow his team-mate to cross for Shelvey - picked as a nominal striker despite just five goals in 52 previous matches for the club - to head in from three yards.
Early in the second half Cole had another chance from Suso's through-ball but Wolfli smothered his shot and Young Boys raced down the other end to equalise.
Henderson was caught on his heels when the long, diagonal pass came over to Bobadilla and he controlled the ball on his right thigh and in the next movement smashed an unstoppable left-footed drive past Jose Reina.
The arrival of Luis Suarez was not delayed much longer and when he replaced Suso new life was breathed into the Reds' forward line.
Few would have suspected Suarez's magic dust would have rubbed on Cole but the 31-year-old rolled back the years, as well as his marker, to turn on the pass supplied by Gerrard via the Uruguayan and plant a shot past Wolfli.
But he was denied his moment of glory by Zverotic's swerving 88th-minute strike.