FC Basel overtook them on goal difference by beating Neuchatel Xamax 3-0, helped by two goals from Switzerland's record international scorer Alexander Frei.
Young Boys, runners-up in the last two seasons, will host Basel on Sunday in their final match, needing a win to clinch their first title since 1985/86.
Both teams have 77 points from 35 games and have already made sure of places in the Champions League qualifying rounds next season.
Luzern's win clinched a fourth-place finish, which gives them a place in the Europa League qualifiers along with third-placed Grasshoppers.
Nelson Ferreira, Cristian Iano and Burim Kukeli scored as Luzern raced to a 3-0 halftime lead on a treacherous rain-soaked pitch at their ramshackle ground, before Iano and Nico Siegrist added two more in the second half.
Young Boys' consolation was one of the best goals of the season, Ivorian striker Seydou Doumbia leaving six defenders in his wake before rounding the goalkeeper to score his 30th goal of the championship.
Frei's goals were his first for Basel since recovering from a broken arm in February and took his tally to 15. The 30-year-old, who has 40 goals in 73 appearances for Switzerland, is set to lead their attack at next month's World Cup.
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