Piazza was born and raised in Queens, New York. His father is Italian, having immigrated to the U.S. in the early 1960s. His mother is of German descent. Piazza played ACHA Division I ice hockey for Villanova University in Villanova, Pennsylvania, until a recurring shoulder injury forced him to quit playing and leave the university after only a year. After retiring from hockey, he began to work with acting coach Alice Spivak and joined the TerraNOVA Collective theatre group in Lion Theatre along Theatre Row in New York City. After appearing in a number of New York Off Broadway productions, including Baby Steps, A Match Made in Manhattan and Much Ado About Nothing, he made his feature film debut in the Stephanie Daley and went on to appear in the television movie The Dawn and an episode of Law & Order: Criminal Intent.
Piazza has appeared in three episodes of the television series The Sopranos; the eighth, eleventh and thirteenth episodes of the show's sixth season. He describes his experience working on the show as incredible and says he would appear in any prequels or sequels to the series if he was asked. He then featured in the film Rocket Science as Earl Hefner, the kleptomaniac older brother of the film's protagonist. After auditioning at a casting session held at a New York acting school, he ended up being one of the first actors cast, writer-director Jeffrey Blitz saying: Vince brought just the right combination of humor and threat to the part ... kept many of the rest of the choices Vince brought to Earl. He’s a very physical actor and a very funny one, too. He went on to appear in the independent films Goodbye Baby, Tie a Yellow Ribbon and Apology, as well as guest-starring in an episode of Law & Order, before he landed the recurring role of Tony in Rescue Me's fourth season.
Piazza appeared in the film Assassination of a High School President in the role of Ricky Delacruz..

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