All seemed lost when Park surrendered a 12-0 lead and the visitors from Wakefield hit the front for the first time against towering opponents.
However, White sold an outrageous dummy, ghosted through the Crigglestone defence and raced 50 yards to snatch victory.
Park had their tackling and some fine long kicks from Lee Brook to thank for being in the hunt up to then.
Crigglestone looked quicker with the ball in hand but were knocked out of their stride by some big hits with home forwards Nathan Raynor, Andy Boocock and Craig Syme working overtime.
Park took the lead with a well-worked move, Brook and White setting up Matthew Brown.
Brook's kicks drove Crigglestone back while young fullback Jacob Hyde pulled off a great tackle to stop a wingman in the corner.
Park went 8-0 up when White and Adam Barrett did the spadework for Brook to touch down and Luke Brown then went through a gap to make it 12-0.
However, Crigglestone scored two unconverted tries of their own and had Park on the back foot.
The visitors' fullback made a mess of fielding Danny Fearon's long kick, enabling Brown to score his second, but Crigglestone hit the front at 18-16 when a wingman scored wide out and they grabbed another try.
However, with time running out, White came to the home side's rescue.

Elland A 20 - Keighley Albion 6
(Andrew Bennett Trophy)
ELLAND produced another superb performance in atrocious weather.
Playing into a howling wind in the first half, the young Elland side moved the ball around, stretching Keighley's defence on a number of occasions.
Half backs Brad Pearson and Chyle Fisher combined to create an overlap to put Gaz Saltonstall over for the first try.
Elland continued to defend well with Ben Manning and Dave Webb tackling everything Keighley could throw at them.
A well worked move by Elland saw the ball spread wide and good inter passing by Lee Childs and Darren Brown resulted in Childs scoring, Fisher converting.
The elements meant Elland were unable to convert other chances and they went into half time leading 10-0.
Elland created more chances spoilt by the elements to go in 10-0 at half time.
The home side piled on pressure after the break and hard working hooker Webb went over from acting half.
Keighley defended admirably but man of the match Manning forced an error and from the resulting scrum fullback Dean Bishop finished off a set move. Fisher converted.
The only blot on Elland's copy book was a late consolation try by Keighley.