Spectators at Holloways Park would be forgiven for calling the opening period of the game a dire affair, and the opening quarter of an hour produced no chances of note.
Of the two teams, Slough always looked the most likely to break the deadlock, and Burnell could have had a clear shooting chance had his touch been better as Coyne clipped a ball through to the striker, who was onside.
Slough had James Warrington to thank early on though, the Rebels stopper bravely diving in to deny striker Reis Stanislaus a scoring chance.
Sinclair fired a shot over the angle from the edge of the box, and Dave Woozley headed a Paul Coyne free kick wide of the post as Slough continued to press.
Burnell went closer still as he lashed home after being played in by Chris Herron, but the effort was ruled out for offside.
But Stanislaus gave the visiting Peacocks a 28th-minute lead with a header which looped over James Warrington, following a good move and dangerous cross from Shaun Lucien – Steve Sinclair’s desperate attempt to keep the ball out being to no avail.
Bedfont’s ambition reduced significantly following the opening goal, and Paul Coyne almost notched a fortuitous equaliser when his free kick to the far post went all the way through, and hit the inside of the post before being gathered by goalkeeper Gary Ross.
However Slough did go into the half-time break level, with Alex Brown registering his first goal for the Rebels. The big defender ignored the pushing and shoving from Ross and his fellow defenders, and got his head to Coyne’s corner to send it beyond the goalkeeper.
Slough enjoyed by far the better of the second half, but really struggled to break down their opponents. Bedfont’s Lucien went on a storming run through the heart of the Slough defence which led to Stanislaus firing well wide, and full-back Dan Carter blazed over from the edge of the box, but the visitors carried little threat.
It felt as if Slough just hadn’t got into their rhythm at any point during the game, but still looked most likely to create something – and Burnell had a good chance to do so, but, having got into a great position, was narrowly unable to get sufficient contact on Steve Sinclair’s whipped cross.
Bedfont were clearly happy to settle for a point, and with the home support urging them on, Slough became increasingly frustrated at not being able to get in behind a shaky-looking defence.
However, the Rebels looked to have been given a lifeline with eight minutes remaining, as referee Adam Fielding spotted a handball offence in the box after Chris Herron had swung in a free kick. Burnell stepped up and, after a slight delay caused by Bedfont defenders looking to encroach into the box, agonisingly side footed his kick over Gary Ross's bar.
It looked as if Slough’s chance had passed, but even later drama was to follow. Great work by Sonner saw him keep the ball alive and cross into the middle, where Ollie Burgess hit a rising drive which Ross had to tip over.
Moments later, substitute Stuart Swift's fierce volley was handled on its way through to the goal by defender Jon-Barrie Bates, and Fielding again pointed to the spot, allowing Burnell a second bite of the cherry. This time the Rebels top scorer made no mistake, firing low to Ross's right and sealing another vital victory.
Bedfont Town Line up
Gary Ross, Dwain Williams, Dan Carter, Matt O'Brien, Joseph Otaro, Jon-Barrie Bates (c), Shaun Lucien, Davis Haule, Reis Stanislaus, Glen Garner, Wayne O'Sullivan. Subs: Byron Bubb, Danilson Vicente, Aaron Coldman, Daniel Ranger, Lee Scott.