Harris, returning to the starting line-up after serving the first of a two-match ban on Saturday, provided the two magic moments of a tight contest between the two National League South rivals.
Hungerford made the brighter start to the game, with captain Richie Whittingham pulling the strings in midfield. Slough got more of a grip on the game as the first half progressed, fashioning their first chance.
The hosts failed to fully clear a corner, and Slough recycled the ball back into the box and found Ben Harris at the back post, but he put a headed effort off target.
Soon after, Tommy Ouldridge volleyed a spectacular effort into the top corner, but the goal was ruled out for offside.
Further Slough chances fell to Ben Harris, who headed off target again, and Josh Jackman – playing at left-back on the night – with goalkeeper Charlie McCready diving low to keep out his effort.
Harris also hit a post, with Jackman following up and having a shot blocked, but Hungerford cleared and made it to half time unscathed.
Slough had the better of the second half in terms of ball possession, but found the Crusaders hard to break down.
However, Harris changed that by scoring a superb individual effort from outside the box. He beat two or three Hungerford defenders before rifling a beautiful effort into the back of the net with his left foot to give the Rebels the lead.
Slough looked for a second goal but could not convert their pressure into a threat to McCready’s goal – and the hosts looked to have taken the game to a penalty shootout when they equalised ten minutes from time.
Whittingham played a free kick into the box and found Danilo Orsi-Dadomo, who struck the ball home at the far post.
But Harris struck again as the game moved into stoppage time, with the winning goal almost a carbon copy of his FA Cup strike at Eastbourne. Harris looked up and from fully 50 yards, floated the ball over McCready to send Slough through.
Harris had one final chance to complete a hat-trick, but hit the woodwork for the second time with seconds remaining.
Hungerford Town Line up
Charlie McCready, Marcus Johnson-Schuster, Matt Jones, Dan Bailey, Tarik Moore-Azille, James Rusby, Tommy Ouldridge, Alfy Whittingham, Danilo Orsi-Dadomo, Richie Whittingham (c), Darren Foxley. Substitutes: Josh Elms, Tommy Rees, Charlie Ten-Grotenhuis, Ian Herring.