United got off to the best possible start with a goal after just 90 seconds as a Wes Tate corner found Jason Taylor 20 yards from goal, who proceeded to rifle his effort past James Fisher despite the 'keepers best efforts.
Most of the early exchanges went in United's favour with numerous shots blocked and corners won as a result.
Taylor saw a carbon copy of his earlier goal deflected wide, with Lucas Mann and Bailo Camara also denied.
Broadbridge Heath saw their best effort of the half fall to Ollie Moore, who swivelled inside the area but his effort failed to trouble Russ Tanner and flew over the bar.
Taylor found himself through on goal towards the end of the first half after a flick from Mann, but Matt Carruthers stopped the United man in his tracks after knocking the ball past Fisher.
Camara and Taylor were a constant thorn in the side of the Heath defence all afternoon and the former came close to extending the lead, but his header was too high to trouble Fisher.
With just over ten minutes remaining, Lucas Mann was brought down inside the area by Fisher, who recieved a yellow card for his troubles and United were awarded a penalty.
Up stepped Wes Tate to send Fisher the wrong way as United made it three clean sheets in a row.