Gavin James threatened the home goal after six minutes with an effort which was tipped over, but the Rebels suffered a blow minutes later as Lewis Putman was forced off with an injury, and he was replaced by James Dobson.
Simon Dunn curled a shot over and Harrow responded with a long distance shot which was blocked and gathered by Mark Scott. The Rebels went close again as James was played through by Nathan Webb. James' shot was blocked, with Warren Harris having a follow-up effort saved.
Shortly after putting a 25-yard effort just over, left winger Dobson crossed in from the wing and Charlie Moone turned and fired past the Harrow goalkeeper.
Dobson and Moone combined again shortly before the interval, but Moone's header was held by the keeper.
Harrow started the second half as the better side with a couple of efforts not far wide of Mark Scott's goal, and a header narrowly missed the goal at the near post on the hour mark.
Slough doubled their lead on 77 minutes when Barney beat two challenges and saw his shot saved, but the ball fell straight to James, who tapped the ball home.
The hosts went close a minute from time when a free kick was flicked on, forcing a superb one-handed save from Scott.
Slough Town Line up
Mark Scott, Sean Fraser (c), Paul Stonehouse, Guy Hollis (Josh Jackman), Mark Nisbet, Nathan Webb (Lee Togwell), Lewis Putman (James Dobson), Simon Dunn (Adrian Sear), Gavin James, Charlie Moone (Lee Barney), Warren Harris. Sub not used: Brad Hewitt.