Spurs' two away goals keep alive their hopes of qualifying for the prestigious competition as the second leg takes place at White Hart Lane on August 25th.
Young Boys earned a three-goal lead in the first half when Senad Lulic, Henri Bienvenu and Xavier Hochstrasser scored on four, 13 and 28 minutes respectively.
Tottenham's Sebastien Bassong pulled one back in the 42nd minute before Roman Pavlyuchenko gave the Premiership side a new hope with another strike seven minutes from time.
Elsewhere, four-time European champions Ajax played out a 1-1 draw at Dynamo Kiev.
The Dutch side should easily reach the Champions League group stage as their next playoff is to be held in Holland late this month.
Jan Vertonghen put Ajax ahead three minutes from the hour mark before Oleh Husyev restored parity on 66 minutes.