Slough, much-changed from last season when the club avoided relegation due to reorganisations in other leagues, were looking to prove that they will be challenging at the other end of the table, whilst Burnham were looking to start the new campaign well and improve on last season where they narrowly missed out on a play-off place.
The Rebels almost got off to the worst possible start though, as inside two minutes, Jordan Dowdican burst through the Slough defence and saw his shot beat Jamie Jackson but hit the far post.
Slough rallied and enjoyed a good spell of possession and a great move involving skipper James Pritchard and John Gray ended with the former testing former Rebel Michael Parkin from just inside the area.
Steve Daly then saw a headed effort ruled out for a push before Ryan Fenton pulled off a remarkable goal-line clearance at the other end. Dowdican again was causing problems, and the striker left the defence for dead and lifted the ball over Jackson, only for Fenton to perform heroics to scramble it away.
The first goal at Holloways Park this season arrived minutes later with Dean Harper the scorer. Danny Jordan found himself in space from a corner and saw two efforts in quick succession parried by Parkin, with Harper in the right place to fire home the rebound on 14 minutes.
Burnham fought back strongly with a sustained period of pressure and grabbed an equaliser fifteen minutes later. Nick Jackson lifted a ball over the top of the Rebels back line and Jamie Handscombe slotted the ball into the bottom corner to level matters.
The teams went in level at half time, but not before a couple of scares for both 'keepers. Burnham hit the post from a curled free kick which left Jackson statuesque, and Slough's Adam Dickens was just wide with a long shot. Jackson had to rush out of his goal to tackle Dowdican outside the box as he broke through moments before half time.
It didn't take long for Slough to go back in front in the second half, with a debut goal from Matthew Platt.
A poor clearance from Parkin fell straight to Danny Jordan, who rounded the 'keeper and squared the ball to Platt in the middle for a tap-in.
A moment of controversy arose as John Gray looked to have been tripped in the box after being put through by Platt. The Slough fans behind the goal appealed along with the players, but referee Redmond waved play on.
The game flowed from end to end in the second half, with few chances being created as neither side could get on top.
Burnham upped the tempo in the final quarter of an hour and were rewarded with a stunning equalising goal.
Efforts from Jackson and Montgomery had earlier missed the target, but substitute Leon Yarnie made no mistake with five minutes to go. The powerful striker picked the ball up just outside the Slough area and unleashed a left-footed thunderbolt which found the top corner with Jackson unable to get a hand to the ball.
It proved to be enough to earn the visitors a point in what was a fair result and an encouraging start to the season for Slough despite the late goal.
Burnham Line up
Parkin, Gill, Owens, Bird, Canavan, Jackson (Brown), Montgomery, Willment Â©, Dowdican (Froud), Handscombe (Yarnie), Huddell. Subs not used: Durrant, Southerden.