Hazlewood came out of comics fandom, with one of his first published art credits being in FOOM #4 (1974), the last issue of that Marvel Comics-published fan magazine to be edited by Jim Steranko.
Hazlewood latched on with DC Comics in 1988 as the regular inker for the new title Animal Man, written by Grant Morrison.
During this period, Hazlewood worked for the British company Fleetway, publisher of 2000 AD, as a cover inker for the title Psi-Judge Anderson.
In the early 1990s Hazlewood freelanced for Fleetway, Eclipse, and Marvel Comics, and in 1991 became the regular inker on DC's Adventures of Superman.
From there, he moved to DC's Doom Patrol vol.4 (2004–2006), inking John Byrne for the book's entire 18-issue run.