As has been the case previously this season, Unted hit the self destruct button when firmly in control and dropped points as a result.
There were two changes to the side that defeated AFC Uckfield Town on Bank Holiday Monday as Peter Cooper and Mike Ginno came into the starting XI in the places of Scott Taylor and Peter Featherstone.
United began the game well and could have found themselves ahead early on as Lucas Mann made space to fire off a shot from the edge of the area, but he uncharacteristically dragged his effort wide of goal.
Phil Hawkins made a smart save low to the left to deny Heath's Devon Fender from finding the back of the net but further chances came and went for United without really troubling the visiting 'keeper, until the 40th minute when they opened the scoring.
Mann showed some quick and nimble footwork to release strike partner Cooper, who finished with aplomb as he fired the ball into the back of the net.
Further chances came United's way in the opening quarter hour of the second half and the lead was doubled on the hour as Kane Penn picked up a loose ball in the area fired a low effort past the 'keeper from 12 yards for the goal that should have sealed victory.
But, as has the been case already this season, United failed to see out the game as Fender pulled a goal back with fifteen minutes to play as he calmly slotted past Hawkins when through one on one.
Heath then drew level ten minutes later through George Cousins.
The result leaves United with 10 points from their opening five league fixtures, but manager Tobi Hutchison was visibly angry at his teams performance in the final half hour and inability to finish off the game.