Clever play between Shane Tudor and Marc Richards earned the Valiants their first opportunity in the third minute but the former's final shot had too much height.
Hartlepool took advantage of some shambolic defending when James Brown's throughball left Matty Robson clear through on goal to slot the ball into Joe Anyon's bottom left corner from 12 yards.
The home side were denied an equaliser after 15 minutes when Tudor's corner was headed towards goal by Akpo Sodje, but former Vale loanee Richie Humphreys cleared off the line.
Foyle's men almost found themselves two down inside 20 minutes when Humphreys' low cross from the left was turned against the crossbar by captain George Pilkington.
After a long spell of little or nothing from both teams, Vale were awarded a free-kick in the 60th minute that again failed to excite the crowd with Tudor blasting the ball into the stand behind.
Things started to look brighter for the Valiants and they were unlucky not to get an equaliser when Paul Harsley gained ground on his marker to poke the ball onto the post from close range, before Paul Edwards' follow up deflected wide courtesy of Godwin Antwi's block.
Pools almost put the game beyond doubt ten minutes before the final whistle when Humphreys' whipped cross was glanced over the bar by the arriving Brown.
Substitute Danny Whitaker summed up his side's poor performance in the 85th minute when he was gifted plenty of space on the edge of the box only to waste the opportunity.
Brown got a goal of his own to complete a professional away performance when he strolled into the box to place the ball low and beyond the outstretched hand of Anyon.