Prior's 63rd minute free header at the back post from George Francomb's corner helped part-time Wanderers push Pools out of the top seven for the first time this season.
Tom Blair's brilliant low finish with three minutes remaining inside the far corner made sure this was a first trip to the Suit Direct Stadium to remember for Marc White's side.
Dorking, who have lost just one of their last seven games to climb to tenth, had already had the better of the chances but Pete Jameson made excellent stops to deny headers from Dan Gallagher, twice, and Harry Ottaway.
White, whose side have kept three clean sheets in a row away from home, said: "For a club like Dorking to come to iconic places like this and get three points is amazing for us.
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CURRAN HAUNTS NASH 3 AGAIN! FER FOOTBAL GROUP
Savage delight as Macc hold nerve
WILL'S BRACE SPOT ON FOR LIONS'TITLE BID
WILL Longbottom's second-half brace from the penalty spot saw Guiseley beat Hebburn Town - a result which saw them leapfrog the Hornets in the play-off places.
CLARKE ENJOYS INSTANT IMPACT!
Returning boss sees Reds clinch late win
JACKSON STUNNER BOOSTS CLARETS
FARNHAM Town staged a second-half fightback to further cement their position at the top of the Isthmian South Central.
WELLIES ARE ON THE UP AGAIN!
THE terrible Coronavirus outbreak decimated Non-League football in many ways.
BRETT BAGS A QUICK SWITCH
Munyard joins Jammers after Regent
BEES HIT BACK IN CAPITAL THRILLER
NICKE Kabamba scored two penalties inside three second-half minutes as high-flying Barnet fought back to edge out London rivals Dagenham & Redbridge in a seven-goal thriller at Victoria Park.
NOR'S THE MERRIER FOR LATICS
SLICK Oldham Athletic cantered to a resounding victory over Tamworth - but boss Micky Mellon and his management are still demanding more!
JOE'S GOT ROBINS IN THE ZONE!
FREE-SCORING Altrincham made it five matches unbeaten as they comfortably beat struggling Southend United to close in on the playoff spots.
SHAYMEN ARE HOTI TO TROT
TEN-MAN Yeovil Town found FC Halifax unbreachable Town despite concerted efforts as the Shaymen edged this battle of National League play-off contenders at Huish Park.