Dog Inn manager Simon Kerins saw his side snatch a point with a stoppage-time penalty, but still maintained it was a case of two points dropped at Memorial Park.
Dog thought they had taken the lead inside 20 minutes, but Josh Holgate’s tap-in was disallowed by the referee after being vociferously disputed by the hosts.
Debutant Matt Sedgwick then headed Dog in front, but a freak own goal and sloppy back pass ushered Harwood into an undeserved lead.
Travis Blezard then netted a penalty to draw Dog level shortly before half-time.
Another freak clearance allowed Harwood to regain the lead early in the second half, and they looked set to hold on before Blezard was felled two minutes into stoppage time.
He picked himself to net Dog’s first point in four games.
Dog captain Dave Dewhurst was named man of the match.
Kerins said: “The decision to disallow Josh’s goal was crazy, but we didn’t do enough in terms of testing their keeper.
“Travis deserves top marks for his composure, but I still feel deflated.”