Sub Jon Quinn scored the winning goal for the visitors.
Park will make the trip to sixth-placed Redcar Athletic Reserves on Saturday, looking to pull away from the relegation zone.
Ten-man Staithes Athletic suffered an 8-1 reverse at league leaders Yarm & Eaglescliffe.
Conor Dunn was dismissed for the visitors, whose consolation was an own goal.
Staithes, who are sat at the bottom of the league table without a win this season, will play host to second-from-bottom side Kader this Saturday, 2pm kick-off.
Whitby Fishermen’s Society entertain Lealholm in a Division One East clash this Saturday.
Goldsborough United earned a 4-1 home win against Duncombe Park Reserves in Beckett League Division Two.
Whitby Fishermen’s Society Reserves suffered an 8-1 loss at home to Gillamoor.
The Fishermen’s second string play host to Duncombe Park Reserves on Saturday afternoon, 2pm kick-off.
Nine-man Sleights lost 2-1 at Ryedale Sports Club in Division One.
Goalkeeper Dylan Humble and defender Sheldon Hegarty were both dismissed for the visitors, who at one point only had eight men on the pitch with Charlie Smith also being sin-binned by the referee.
The villagers fell behind early on but levelled through Sam Russell.
Liam Rissen then had a great goal disallowed for a foul that referee Kevin Crick spotted in the build up.
A late penalty then gave Ryedale the win.
The Sleights man of the match was Sam Bouvet.
Sleights will make the trip to Kirkdale United this Saturday.