Dereham put in a fully committed performance and left the Texo Stadium with a deserved victory with Joe Gatting's opener and a brace from Danny Beaumont doing the damage.
After a sloppy start by both teams with passes going astray, James Grant could not get enough power in to his header from Beaumont's deep free-kick before Robbie Linford's drive was deflected for a corner in the 17th minute.
As Dereham began to brighten, Beaumont worked his way to the left touchline and delivered a perfect cross, allowing Gatting to firmly head home from 10 yards and give the Magpies a 22nd-minute lead.
Heybridge had their first chance when George Cole cut inside from the left and hit an excellent 20-yarder that forced visiting keeper Will Viner into an acrobatic fingertip save. Dereham replied with Will Sainsbury-Logan volleying Vadim Costandachi's ball from the right, inches over the top.
In the 40th minute Heybridge were awarded a free-kick for what was interpreted as a back pass when Costandachi intercepted a pass from the right. The ball was touched to George Cole who drilled a fierce drive into the roof of the net to give the Swifts an equaliser at the break.
After the restart Jack Smith headed Harry Morgan's centre wide for the hosts before Beaumont shot into the side netting. As the Magpies pressed again Dan Morphew's firm header from Beaumont's corner struck a defender and flew behind.
Hinton then had a close-range effort cleared off the line by Mallardo following Linford's chip forward. Dereham upped the tempo and pressed hard to regain the lead. They were rewarded when Beaumont steered home Hinton's header into his path from Logan's cross with 73 minutes on the clock.
The impressive Gatting was fouled outside the box. From the resultant free-kick Beaumont struck a superb curler that rounded the wall and entered the bottom corner for his second and Dereham's third in the 83rd minute.
Heybridge: D Sambridge, M Andrews, G Ramon, H Morgan, S Mallardo, P Anderson, N Brown, L Godbold, J Eaton-Collins (R Grant 61), G Cole, J Smith (J Sykes 61). Subs: L Dark, G Little, R Baker
Dereham: W Viner, V Costandachi, J Grant, R Linford, D Frary, D Morphew, R Logan, D Hinton, J Gatting (J Frohawk 90), W Sainsbury-Logan, D Beaumont. Subs: R Crisp, J Ramm
Ref: Mr C Francis
Attendance: 123
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