Pool made an immediate impact after only 70 seconds when Adam Boyd did well to cut in from the left and supply Joel Porter with an easy chance to blast past a helpless Mark Goodlad.
The visitors almost doubled their lead only three minutes later when defender Michael Nelson attempted an overhead kick, but unfortunately for his side the ball bounced back off the crossbar.
Vale finally got a chance to shoot after 25 minutes, but when Christopher Birchall set up Tommy Widdrington, the veteran volleyed wide.
Goodlad was called into action again on 29 minutes when slack defending allowed Porter an opportunity, but a good save and a poor finish kept the home side in the game.
Former Sheffield Wednesday star Richie Humphreys had another go seconds later but again poor finishing prevented a goal.
The Valiants pushed forward after the break with a change of formation but a lack of fire power upfront meant no threat to a resolute Hartlepool defence.
Martin Foyle's side's best chance came on 83 minutes when Dimitrios Konstantopoulos fumbled a cross, leaving an open goal, but no-one could shoot through the crowd of players.
The away side could have added another at the death but Boyd's long-range drive did no further damage.