The away side had the brighter start to the game, and just eight minutes in Jake Evans almost broke the deadlock as he chipped the ball past North but it went just wide of the post.
The opening goal for Hungerford came inside 15 minutes as Duane Ofori-Acheampong scored his first of the game, finishing well after a Slough clearance deflected right into his path.
Slough had two key chances from crosses within the next 10 minutes from Max Worsfold and Lee Togwell, but were unable to find the target.
Just before the interval Hungerford came close to doubling their lead, as a throw fell to Tyler who shot inside the box but it went straight to North who did well to save it.
But Hungerford went on to double their lead on the 57th minute as Ofori-Acheampong doubled his tally for the afternoon with a strike which took a massive deflection off Freddie Grant.
This came just after Alfonso Tenconi was introduced for the Rebels, which proved to be an important change later on.
With 13 minutes to go, Slough found a goal out of nowhere as Tenconi buried the ball from close range after keeper Luke Cairney spilled a shot from Josh Jackman.
Then just under two minutes later, Slough equalised with a goal from Imran Kayani, who scored his first goal at National League South level as he showed great composure to control the ball as it fell his way from Aaron Kuhl’s cross before placing it past Cairney.
With five minutes to go before additional time, Hungerford had a free kick just outside the box, which Slough were able to block for a corner and defend well to clear the ball out of play.
Then just before the final whistle Hungerford had yet another chance as George Smith headed the ball, but he was unable to keep it down.
The Rebels are straight back in action this Tuesday evening at Arbour Park, with Dulwich Hamlet the visitors.
Hungerford Town Line up
Luke Cairney, Curtis Angell, James Rusby, Duane Ofori-Acheampong (Sol Wanjau-Smith 88), Ryan Seager, Jake Evans, George Smith, Max Ram, Rhys Tyler, Andre Burley (Louis McGrory 75), Kyle Bailey. Unused substitutes: Matt Jones, Nana Kyei, Bruno Tavares.