But Halifax had much the better of the next 15 minutes, using the wind to good advantage and playing with aggression in the forwards.
Two tries resulted, in quick succession, and Park trailed 3-12, looking distinctly second best.
However, Sedgley bounced back and a good period of play was rewarded with an Alex Youngman try which Glynn converted.
Halifax scored another try from a driving maul but Sedgley's backs were beginning to show their class.
A break by Ross Bullough went unrewarded before another one by his co-centre David Mold resulted in a try for the supporting David Livesey. Glynns conversion made it 17-17 at half-time.
Sedgley's backs scored two fine tries at the start of the second half.
The forwards paved the way for the first, a great driving maul from the 22, and then a sweeping handling move finished off by winger Guy Stringer.
Molds long pass then put Glen Stevens over in the opposite corner, and Park led 27-17.
Halifax closed the gap to three points through a penalty try as Sedgley dragged down a maul near their line, but the home team hit back at once as Bullough ghosted through to score at the posts; Mold converted, Glynn having limped off injured.
The final 10 minutes were not the best but this did not detract from a good game on a foul night.
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