Despite having played at Hailsham Town less than 48 hours previously, the United line up showed just one change with Shaun Lee starting in place of Lucas Mann, meaning Jamie Bunn returned to a more familiar midfield role.
United's James Broadbent was the busier of the two goalkeepers in the opening 45 minutes, but he was more than equal to all that the Heath attack could throw his way.
Broadbent had to be alert to push a close range header from Jake Holmes over the bar, before later denying Tim Martin with his feet in a smart stop.
Chances were at a premium for United in the first half, but they became easier to come by in the second half.
Adam Davidson, who was soon after subsituted due to injury, saw an effort turned away by Elliot Flack in the Heath goal before Bailo Camara cut in from the wing and drove at the Heath defence, but was only able to pull his effort wide of the goal.
At the other end, Holmes came inches away from given the Bears the lead as his half-volley saw Broadbent beaten, but his effort went out for a goal kick.
Dave Smart struck his now obligitory  long-range effort that saw Flack equal to the effort, but soon after United were ahead.
Smart was again involved as his corner kick found an unmarked Shaun Lee who headed of from six yards for his first goal since returning to the club
The game was made safe inside the final ten minutes of the contest as Smart struck a low effort from 25 yards that nestled in the far corner to extend United's recent good run of form.