Tuesday night’s win meant the Bears overtook their opponents and rose up to fifth after beginning the game lagging a point behind.
Dan Attwater gave Heath the lead in the third minute when he headed in Grant Miller’s free-kick.
However Midhurst got back into the game on the half hour with with a well-timed effort which was crossed to the near post and put away by Gary Norgate.
Jamal Sultan scored Heath’s 60th minute winner with a fine move begun by Damon Aston with a run down the left flank followed by a cross to the far post where Sultan pounced.
Heath’s delighted secretary Andy Crisp reckoned the victory keeps their promotion hopes alive.
He praised: “It was a good win which keeps us clinging on with an outside chance.
“It was good to have Grant Miller back in the side after a lengthy absence through injury and it was his free-kick which set-up our first goal.
“It was a very niggly game in which we were the better side for the first 20 minutes and then Midhurst got back into the match.
“At times the play fell a bit flat with neither side creating much, but overall it was a very good win.”
Keeper James Fisher made a fine last-minute dive to tip over a shot by Norgate.
Heath: Fisher, Swaine, Etherington, Attwater, Flack, Arthur, Bolaji, Sultan (Martin 82), Miller (Woods 75), Aston, Holmes. Unused sub: Moore