Goals conceded deep into stoppage time at the end of each half saw New Mills make the long trip home from Bridlington with nothing to show for their efforts.
The Millers had taken the lead after six minutes when Hampson was brought down on the edge of the area and Grimshaw’s free-kick to the back post was headed home by Danny Shaw.
The lead was doubled after 23 minutes when Welsby ran down the right and crossed into the area. The ball came loose to Ryan Hopper some 20 yards from goal and his shot was rifled home.
New Mills looked good value for their lead until the 47th minute when Shenton brought down a Scarborough player for a penalty which was duly despatched by Jimmy Beadle.
Then deep into first-half stoppage time, the full-back popped up again to net his second, heading his side level.
The Millers had plenty of defending to do in the second half and did it well, creating several goalscoring chances in the process.
In fact they were looking the more likely to get the winner until Scarborough made a break in the 94th minute and Gary Bradshaw fired in a shot across Collinge.
New Mills: Collinge, Shaw, Fitton, Parsons, Shenton, Wood, Hopper, Welsby (Hynes), Hampson (Bancroft), Smith (Dominic Marie), Grimshaw. Unused subs: Howell, Green.