Kilkenny protested his innocence and had to be persuaded to leave the field as his manager Simon Grayson remonstrated with referee Andy Madley.
Neal's opposite number Declan Rudd produced a brilliant save to deny Tom Pope a minute later, but that was Vale's only serious threat of the first half.
Vale drove forward in search of an equaliser after the interval but got caught on the break when Neal conceded a 71st-minute penalty for tripping substitute Will Hayhurst.
Garner drove the ball low to Neal's right to net his seventh goal in five games and Preston then defended impressively to see out the game in comfort.
- Sports & Recreation
- Chris Neal
- Neil Kilkenny
- Simon Grayson