Avanzino had wanted to be a comic book artist after graduating from high school, but instead studied architecture; he started in the animation industry at Klasky Csupo to work for the second season of The Simpsons. He would work on the series intermittently as part of Rough Draft Studios until 2004.
After Klasky Csupo had their Simpsons contract terminated by Gracie Films in favor of Film Roman, Avanzino moved to Spümcø to work for The Ren & Stimpy Show; he was one of the few hires at the studio early on during production of the second season. He served as a storyboard artist in episodes in the second season, storyboarding "Son of Stimpy"; after John Kricfalusi and Spümcø were fired for negligence, he transferred to Games Animation with his peers and directed "Stimpy's Fan Club", one of the series' most critically acclaimed episodes in place of Kricfalusi. He stayed in the series as a storyboard artist until the fourth season. He would rejoin Klasky Csupo to work on The Wild Thornberrys and Duckman before finally settling at Rough Draft Studios in 1998, having been acquainted with the studio while at Games Animation.
As part of Rough Draft Studios, he would serve as storyboard artist and later director for Futurama; he had described it as one of his favorite working experiences, continuing work on the show to this day. Aside from collaborations with 20th Television (Animation), he had also directed the first season of Clash-A-Rama!, which Rough Draft Studios produced on commission by Supercell based on their video game Clash of Clans. Owing to his connection to Matt Groening he had also worked on Disenchantment.
