The two sides went into the clash level on 54 points, but Harrison settled the match in favour of the visitors, moving them up to sixth.
Chesterfield looked the brighter of the two teams during the early exchanges, Gary Roberts going close with an ambitious 45-yard effort, before Sam Clucas' volley flew just wide after 24 minutes.
Bradford did come into the contest, though, and Harrison scored on the stroke of half-time.
The forward latched on to Gary MacKenzie's tame headed back-pass and kept his cool to slot in after skipping beyond goalkeeper Ben Williams.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.