Dario Gradi ended his spell as Crewe's caretaker boss by guiding the division's bottom side to their first away win in the league this season.
John Brayford forced the ball home from close range in the dying seconds of the first half, only for Joel Porter to level for Hartlepool after the restart.
Crewe regained the lead when Michael Nelson put through his own net.
Luke Murphy's 20-yarder into the top corner made it 3-1 before an easy finish for Shaun Miller sealed the win.
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