Young Boys, who last won the title in 1986, were also left to contemplate the runners-up spot for the third season running while Basel completed a league and cup double in their first season under German coach Thorsten Fink.
Basel went top on goal difference last Thursday after Young Boys slumped to a 5-1 defeat at FC Luzern and, with the fixture list throwing the pair together in the final match of the season, Basel needed only a draw at the Stade de Suisse.
Scott Chipperfield headed the second in the 61st minute from Stocker's cross, although the Australia midfielder was lucky to escape injury when he failed to clear an advertising board in his celebration and fell flat on his face.
Young Boys' frustration boiled over and Stocker, picked for Switzerland's World Cup squad, was stretchered off after being hacked down.
