Vale Park bathed in bright sunshine at kick-off and both sides soon warmed to the task.
Tobias Mikaelsson, on loan from Aston Villa, threatened to open his account for Vale in the eighth minute when his powerful strike was well saved by Kieren Westwood.
But Carlisle looked determined to break their away hoodoo with Simon Hackney and Evan Horwood eager to get at Vale's shaky defence.
Horwood went close in the 27th minute when his low cross-cum-shot dribbled inches wide of Joe Anyon's left-hand post.
But Vale's response was quick as Horwood charged down a close-range shot from Harsley seconds before David Howland's 20-yard cracker forced more acrobatics from Westwood.
Mikaelsson shot wide early in the second period and Carlisle's attacking efforts continued to lack sting as Scott Dobie's header failed to trouble Anyon.
Former Vale man Marc Bridge-Wilkinson also lifted a 20-yard free-kick way over the bar much to the amusement of the home supporters.
But Carlisle top-scorer Joe Garner was foiled by the onrushing Anyon on the hour before the breakthrough came two minutes later.
Vale defender George Pilkington was caught out by Westwood's long clearance and his wayward header was volleyed home in style by Garner for his 14th goal of the campaign.
The goal was Carlisle's first away from home for eight hours and 55 minutes and ended a run of five successive defeats on the road.
Vale looked to be heading for their 20th defeat of the campaign until Peter Murphy manhandled Kyle Perry and Harsley made no mistake from the spot.