Dominic Gentle's injury time penalty saw Heybridge snatch all three points from Saturday's visit to Essex rivals Billericay.
A sizeable New Lodge crowd of 685 saw both sides struggle to gain the advantage over the first half-hour with resolute defending at both ends leaving attacking play at a premium.
Billericay did though take the lead on 34 minutes when Martin Carthy was clumsily brought down in the penalty area and Joe Baker tucked the ball home.
Tim Cole then went close with a free-kick that threatened to snap the crossbar, and as the second half progressed, the match looked increasingly likely to finish with the home team taking all three points.
However, with five minutes left to play, a dangerous spinning ball was swung in and John Pollard, up from the back, nodded home the equaliser.
Into injury time, and Cole was adjudged to have unfairly brought down Jamie Window. Gentle kept his nerve to fire home and take the points for Swifts who climb to 14th in the table; Billericay remain 8th.
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