Dogged hosts Redditch played with commitment and desire that defied their position ominously above the relegation zone.
But Park, for the second time this season, earned a late winning try to land win number 13.
Playing into a stiff wind, low sun and on a rapidly deteriorating pitch, Park struggled for fluency and accuracy.
Joe Graham seemed destined to extend his try-scoring sequence with a wonderful break down the left flank but he was thwarted by a high tackle.
The same man broke through a gap from a loose pass to dance upfield to feed Arron Owen who was well tackled.
Jonny Hincks claimed a fine high ball from Dan Joyce's wayward kick but he was fouled by s fine covering tackle.
The flurry of early activity did not yield a score and Redditch grew in confidence.
A spate of penalties ended with a place kick that was pushed just wide for the hosts.
For the first time this season Park failed to score in the first half as the sides were still deadlocked at the interval.
Redditch enjoyed a strong spell after the restart and on 48 minutes went ahead with a simple penalty kick.
This was almost immediately wiped out when Callum Bishop nudged over a penalty from a central position.
Redditch failed to threaten the try line but had the lion's share of possession and territory - as Park were frequently penalised for offences such as crossing and accidental off side.
Park's defence was solid as a rock with Dave Melville and Stephen Ballard putting in some shuddering hits.
As Redditch tired coach Kev Venus brought Matt and Dan Green off the bench as well as Mark Wickett.
Hincks gave Redditch a warning of his threat but his grubber was overhit.
But he wasn't to be denied. Park moved the ball open with Hincks combining with Bishop on the drift. When the latter was caught, Hincks remained alert to receive the offload to run home from inside the 22.
Bishop confidently drilled over the conversion to open a seven point lead with minutes remaining.
Redditch fought upfield but met fierce resistance as Park held on to their advantage.
Coupled with Claverdon's defeat at Atherstone, Venus' side have a 14-point lead at the top of the league.
Third-placed Upton are 15 points behind with a game in hand to reduce that deficit.