The Blues held their higher league opponents throughout the first half but two goals in four minutes early in the second period put United in full control of the pre-season friendly.
The hosts had the first opportunity of the game on 12 minutes when Hayes & Yeading's Tom Cadmore fouled Chris Elsgood just outside the penalty box. However, Lewis Cook's free-kick lacked power and direction allowing Billy Lumley to save comfortably.
Hayes were unfortunate not to take the lead on 19 minutes when Jordan Patrick's low cross found Richard Paquete whose effort was deflected over the cross bar for a corner.
A minute later, Paquete had a second effort deflected off target after the striker had won possession from Dave Reading who got the ball stuck under his feet.
The first bit of quality in the game came on 38 minutes when Hayes & Yeading's Piere Joeseph Dubois' fierce effort was just wide after Burnham's Dean Papali had given the ball away on half.
Shortly after, Ryan Crockford's effort flashed wide after the Blues allowed their opponents too much room in midfield.
The Conference National side eventually took the lead four minutes into the second half when Paquete headed home a Crockford free kick inside the six-yard box. United were awarded the free kick after Nathan Jack had cynically fouled Sam Argent.
Four minutes later, Hayes & Yeading doubled their lead when Julian Owusu was allowed space inside the box to head home Jerome Federico's cross from the right.
The concession of two goals in quick succession had frustrated the home side and referee Mr. Alex Groves had to warn Matt Seedal and Adam Dickens about use of foul language after the pair had been getting at each others throats.
The game was almost put beyond Burnham's reach after lackadaisical defending from Elsegood allowed Federico to burst into the box but his low cross from the right avoided the final goal-bound touch it needed.
The Blues had chances to get back into the game midway through the second half when Liam McManus' volley was on target but straight into the arms of the Unietd keeper.
Shortly after, the substitute stopper punched his clearance into the back of a defenders head and towards goal. Central defender Mark Bentley hooked the ball clear, and despite appeals from Burnham players that the ball had crossed the line, assistant referee Mr. N Mackenzie didn't award the goal.