Briaschi made his professional debut with Vicenza during the 1975–76 season, making 4 appearances in 2 seasons with the club. He was a part of the so-called "Real Vicenza" side, which won the Serie B title during the 1976–77 season, and subsequently finished second in Serie A during the 1977–78 season, playing alongside Paolo Rossi. The following season he found more space and made his UEFA Cup debut. After an unproductive season on loan at Cagliari during the 1979–80 season, he returned to Vicenza for a season, scoring 11 goals in Serie B, which were however unable to help the club avoid relegation. In 1981, he subsequently moved to Serie A side Genoa for three seasons, scoring 29 goals, including 8 during his first season, and 12 during the 1983–84 Serie A season.