The league leaders led 3-0 thanks to Tom Ratcliffe's early penalty, but the hosts battled back and crossed out wide to lead 5-3.
Back came Scarborough, Euan Govier touching down for a try converted by Ratcliffe to give the away side a 10-5 lead.
A penalty and a converted try then handed Park a 15-10 lead heading in at the half-time break.
That lead was trimmed back to 15-13 thanks to the boot of Ratcliffe once again after the interval, but a breakaway try by Park restored their control at 20-13.
A straightforward penalty then further extended Park's dominance, with their lead taken to 23-13.
Scarborough showed the battle and spirit that has seen them battle back on numerous occasions this season, with Aaron Wilson crashing over the Park whitewash and Ratcliffe then converting to make it 23-20 and give the away side hope.
After creeping into injury-time at the end of the 80 minutes, Ratcliffe stepped up to slot home a crucial penalty to seal a dramatic 23-23 draw and a share of the spoils for Simon Smith's men.