Goals in either half from Gary Brazil and Gary Abbott were enough to end any dreams the Shaymen had of a Trophy and Conference double, although George Mulhall's side will at least hope that this was their last ever game in the competition.
Things started badly for Halifax as traffic problems meant that they arrived just 10 minutes before kick-off, with referee Dermot Gallagher insisting the game went ahead on time. But the Shaymen weren't could cold early on, and with Brian Kilcline given a starting role at the back, they weathered the early storm and should have gone ahead in the 11th minute, but Kevin Hulme's header was turned around the post by Paul Wilkerson.
It was the first in a number of excellent saves by the Slough keeper, all of which came at key moments in the match. Slough took the lead through their Gary combination in the 17th minute, as Garry Smart fined in a cross from the right and Abbott flicked the ball back to Brazil, who coped admirably with a tricky bounce to hook the ball in with his left foot. Brazil was an inspiration on the night, as he and Danny Bolt constantly buzzed around the midfield and never let the Shaymen settle into a rhythm.
Slough should have extended their lead in the 33rd minute; but by the time Corey Browne had brought Brazil's superb lob under control, the angle had become too acute and his shot gave keeper Lee Martin no problems.
The Conference leaders had their best chances to level in the two minutes either side of the interval. However, Hulme stabbed his shot from five yards out just wide of the post, and when Geoff Horsfield had only Wilkerson to beat, he struggled with the bobbly surface and the keeper saved with his shins.
The Rebels punished the visitors in the 64th minute, when Halifax keeper Martin waited for Bolt's looping corner to drop into his hands only for Abbott to leap in and head the ball home from a couple of yards out. It took the striker to 11 goals this season, although it was his first since October.
Mulhall threw Kildine up front for the final 10 minutes, but the Rebels hero was Wilkerson, who denied Mark Bradshaw and Hulme with great saves to preserve Slough's margin of victory.
The result was just rewards for the crowd of 876 - Slough's fifth highest of the season which was fairly impressive for a chilly Tuesday night. The Rebels should not underestimate their opponents in the next round. Ryman Leaguers Boreham Wood, but having disposed of the best club in non league football, the Rebels should have no-one to fear in the last 16.
Halifax Town Line up
1. Lee Martin, 2. Andy Thackeray, 3. Mark Bradshaw, 4. Jamie Murphy, 5. Brain Kilcline, 6. Paul Stoneman, 7. Kieran O’Regan, 8. Kevin Hulme, 9. Geoff Horsfield, 10. David Hanson, 11. Jon Brown. Subs: Darren Lyons (for Hanson, 59), 14. Noel Horner (for Horsfield, 68), 15. Michael Midwood (not used).