A brilliant victory away to the league leaders, and Bridges played for an hour with only ten men after Brannon O'Neill was sent-off for a two-footed challenge, quickly followed by manager Paul Faili for protesting.
But it was O'Neill who gave Bridges a ninth minute lead with their first serious attack, working his way into the area before shooting past former Bridges 'keeper Simon Lehkyj.
An early loss to injury of Connor French was quickly followed by O'Neill's dismissal, but Bridges refused to sit back and French's replacement Ben Bacon was only just wide with a snap shot after good work between debutant George Gaskin and the evergreen John Lansdale.
The first half closed with Heath's best player Alex Laing firing a free-kick towards the near post, where Kieron Thorp showed commendable alertness to turn the effort away.
Five minutes into the second half Gaskin forced Lehkyj to a brilliant diving save, but within a minute Bridges had doubled their lead when a corner by Lansdale curled straight into the net!
On the hour came the best goal of the lot when Lansdale's cross was superbly headed in by Nathan Crabb, whose non-stop running made him just one of the many heroes for the visiting side.
But five minutes later a terrific shot by Karly Akehurst was tipped onto the bar by Thorp but fell kindly for Jack Langford to nudge home.
Bacon tested Lehkyj from range and Gaskin wasted a great chance, the ball sticking under his feet as the pitch got progressively wetter and stickier.
It was now the time for Bridges to dig in deep at the back and there was one notable tackle by Nathan Koo Boothe to prevent Heath from staging a late rally.
And a minute into added time Bacon broke from inside his own half and rounded Lehkyj, who had acted as a more than capable sweeper at times, to end with a tap into an empty net for an excellent three points.
And Heath's agonising afternoon was complete when the already substituted Jamie Cradock was shown a second yellow card as the teams came off!
Bridges: Thorp, Collins, Whitehead, Grant, Koo-Boothe, Crellin, Crabb, O'Neill, French (Bacon 24), Gaskin (Peters 85), Lansdale.
Unused subs: Casselman, Berry
Heath : S.Lehkyj, J.Daly (C.Saunders, 61), J.Cradock (B.Rogers, 70), K.Akehurst, J.King, T.Graves, A.Laing, G.Hayward (N.Rouane, 61), J.Langford, K.Louis, J.Weston.
Unused Subs. - C.Weatherstone, M.Newnham.
Aerotron Man of the Match: Nathan Crabb