Carl Baker scored a brace for the Sky Blues with David McGoldrick, Franck Moussa and Adam Barton adding the other goals in an impressive second-half display at Victoria Park.
It was the first time City had ever won an away league game 5-0, and their first-ever win at Hartlepool.
It was also their biggest away win since a 6-1 thrashing of Walsall at the Bescot Stadium in January 2004.
It was the first time Coventry had scored five in a league game since April 2008, while McGoldrick equalled Clarrie Bourton's record of scoring in five consecutive away games.
