Brown opened the scoring for Hartlepool after 20 minutes
Hartlepool punished some slack Cheltenham defending to keep the Robins rooted to the bottom of the table.
Just before the mid-point of the first-half Hartlepool scored twice in three minutes thanks to James Brown's slick finish and an Andy Gallinagh own goal.
Just past the hour Robins keeper Shane Higgs was unable to hold a cross and Andy Monkhouse finished well.
Substitute Michael Mackay scored from a tight angle for the fourth, before Lloyd Owusu's header made it 4-1.
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