Plett was born in Asunción, Paraguay to Russian-German émigré parents; the family moved to Niagara-on-the-Lake, Canada when Willi was a boy. He didn't start playing organized hockey until age 12 although once he caught on, he fell in love with the game. By the time he made the junior level with the St. Catharines Black Hawks of the OHA, he lacked finesse and aggressiveness. As a result, his coach, Hap Emms, demoted him to a tier-two level club.
From that point forward, Plett began to barge around the ice, playing roughhouse hockey.Template:Citation needed It didn't do too much to raise his stock in the draft,Template:Citation needed but the Atlanta Flames picked him up in the 4th round in 1975.
Plett played four games with the Flames before heading to Tulsa for tutelage from a coach who could understand his needs, former NHL enforcer Orland Kurtenbach.
The following season, Plett started the year in Tulsa, but was called back to join the Flames. He made a surprise splash, netting 33 goals and 23 assists in 64 games. He was awarded the Calder Trophy as the league's best rookie. In 1980–81, with the Calgary Flames, Plett scored a career-high 38 goals.
In 1987, the Boston Bruins picked him up in the waiver draft. That season, the Bruins made a solid run in the playoffs, making it to the finals, only to be shut out by the Edmonton Oilers. It was Plett's final game in the NHL. He currently owns a landscaping company in Roswell, Georgia.