With the league being rebranded as the Southern Combination Football League from next season, the three time Division One champions were looking to end on a high, but were handed their 7th home league defeat of the season.
Heath, who had taken 32 points out of a possible 49 away from home this season coming into the game, went ahead in the 22nd minute as Ollie Moore was allowed too much space inside the six yard box to fire past Russ Tanner after a right wing corner.
Moore could have given the visitors a two goal cushion on the half hour as he broke free to take the ball round Tanner, but he was unable to hit the target with his effort.
Unite found chances limited in the opening half, with Jason Taylor seeing a weak header comfortably gathered before Dean Stevens came a posts width away from an equaliser with a glancing header.
Wes Tate dragged an effort wide of the far post after a precise long ball from Dan Pollard, while Taylor was foiled by Heath ‘keeper Andy Howard after a long punt downfield from Tanner.
Tate saw an effort arrow narrowly over the bar after the ball had sat up nicely following an enterprising run from Aaron Capon, before Heath made the game safe in time added on as Jake Holmes calmly slotted past Tanner from 18 yards.
The defeat means that United finish in 12th place on their return to SCFL Division One, with 51 points from their 38 games.