And the Rebels left it very late to seal their progress, with Jack McKnight coolly converting a penalty kick won by substitute Ada Okorogheye two minutes into second half stoppage time.
This was a tight contest in which the Darts had the better of the chances but were unable to beat Jack Turner.
The hosts went closest first as Ronnie Vint met a corner from Gavin McCallum, but he could only head over the bar.
Dartford threatened again minutes later. Jazzi Barnum-Bobb crossed into the box after good work by McCallum. The ball was met by Elliott Romain, who saw his effort deflected into the path of Charlie Sheringham. The striker reacted quickly but probably should have done better than put his effort wide of the post.
Nine minutes in, McCallum dragged a shot wide after cutting in from the left, and Slough then threatened for the first time with Sam Togwell getting his header to a corner played deep into the box, but goalkeeper Craig King caught the ball easily.
The game settled down and Slough created two good chances after the half hour mark. Louis Lomas headed a corner over the bar on 33 minutes, and soon after Paul Hodges went closer still, as he fired just wide after running at the Dartford defence.
In contrast to the first half, the second started at a slower pace. It took nine minutes for either side to work an opening, with McCallum putting in an excellent low cross which Slough were able to clear.
This prompted the Rebels to respond, and Matt Lench fired over the bar from 25 yards after being fed by Hodges. Shortly after, Lench again took aim from the edge of the box, and this time King tipped the ball over.
The lively McKnight was unlucky to see an effort blocked by Vint in the Dartford box on 63 minutes, but the save of the match came three minutes later from Jack Turner. Elliott Romain’s close-range effort was goal bound, but the Slough stopper reacted magnificently to keep the ball out.
Slough freshened things up with Okorogheye and Warren Harris introduced.
With the clock ticking down and minds turning to the possibility of a penalty shootout, Dartford went close again two minutes from the end. Jacob Berkeley-Agyepong drove toward goal but Turner produced another good stop to tip the midfielder’s strike over the bar.
But in the final minute, a corner was cleared only to Okorogheye, who was brought down by Ky Marsh-Brown, giving referee Ben Atkinson no choice but to point to the spot.
The young striker paid the price, having to limp off and leave Slough to play on with ten men - but McKnight made no mistake from the spot, giving Slough a modicum of revenge for July’s playoff defeat at Arbour Park.
Dartford Line up
Craig King, Jazzi Barnum-Bobb, Craig Braham-Barrett, Abdul Osman, Ronnie Vint, Tom Bonner (c), Gavin McCallum, Jacob Berkeley-Agyepong, Elliott Romain, Charlie Sheringham, Noor Husin. Substitutes: Kairo Mitchell, Ethan Wady, David Ijaha, Ricky Modeste, Ky Marsh-Brown, Jordan Wynter, Josh Hill.