A brace from Terry Davies, sandwiching Matt Miller's goal, in the second half set the Rebels up for a remarkable win, only their fourth win in the league all season.
Faced with a Heybridge side who themselves were also in a poor run of form having lost their last four, the Rebels stepped it up in the second half and hung on for the win.
It could have been a far different story if Heybridge had taken their chances in the first half after Danny Bloomfield had given them the lead. Having broken free of the Slough defence, the striker slotted past Jamie Jackson after twenty minutes to put the Swifts in front. Bloomfield and Richard Jolly both missed good chances but the score remained one nil going into the interval.
Slough got lucky with their opener, but you could argue this team's effort has deserved that bit of luck. Davies' effort took a deflection on its way past Danny Gay and into the net to draw the Rebels level.
Slough looked buoyed by the goal and began to apply some real pressure on the home goal and got their reward as Miller robbed the ball off a defender and finished past Gay.
With a lead to defend, the back line looked comfortable against the Swifts attack and will have been disppointed when Gary Burrell was able to win Ian Cousins' cross and finish past Jackson.
This didn't dent Slough's attacking intent and they got themselves back in front as Davies got his second of the game, beating Gay to the ball and finishing well.
Despite a late flurry of pressure from the home side, Slough held on and picked up their first victory since mid-October.
Heybridge Swifts Line up
Danny Gay, Erdem Artun, Ian Cousins (c), Robbie King, Ian Wiles, Dean Chandler, Danny Bloomfield, Michael Alexis, Sean Marks, Richard Jolly, Gary Burrell.