The video was Tom Petty's "Into The Great Wide Open" (1991). However, the girl in the video was Gabrielle Anwar.
The title track to Tom Petty's 1991 reunion with the Heartbreakers introduces us to Eddie, an aspiring musician who hits it big with his debut album, only to watch everything fall apart when he can't deliver the follow-up. In the video, Petty plays our wise narrator (and cameos as Eddie's roadie Bart) while Johnny Depp portrays poor, luckless Eddie. Extending the song's instrumental passages in order to accommodate the video's lengthy rise-then-fall narrative, "Into the Great Wide Open" featured cameos from Faye Dunaway and a pre-Friends Matt LeBlanc. But the video belongs to Depp, who was at his beatific best as the young hotshot who gets chewed up and spit out by the L.A. celebrity machine. This was long before the Pirates of the Caribbean superstardom when he was still one of Hollywood's most beloved bad boys. The song was always meant to be a cautionary tale about fame – with modern eyes, we can see it now applies to Depp just as much as it does Eddie. - Tim Grierson (Rolling Stone)
Depp and Ryder famously began dating after meeting at the New York premiere of Great Balls of Fire! in 1989 when he was 27 and she was 18. They also costarred in the 1990 film Edward Scissorhands.
Remembering Tom Petty: Here 12 of his greatest videos, featured on Billboard.com.