Matthew Maloney delivered an inch perfect ball into the box which Harness guided into the bottom corner of the net, leaving Jonathan North rooted to the spot in goal.
Throughout the contest, Braintree looked dangerous on the counterattack; Gio Crichlow had the goal at his mercy but was denied by sublime North reflexes on 76 minutes.
Stefan Ilic was also causing the Rebels defence problems, playing his part in slick attacking play whilst also having a headed effort saved by North in goal.
It wasn’t all one-way traffic, with Slough starting the game brightly as Tyler Goodrham twisted and turned inside the box with his effort being pushed away by Billy Johnson.
On 19 minutes Imran Kayani whipped in a cross which hit the top of Goodrham’s head after being found unmarked in the Braintree penalty area. A better connection might have tested Johnson.
Midway through the first half, Slough went close to scoring from a corner.
Goodrham delivered a low ball into the near post which Josh Jackman met with a diving header, hitting the outside of the post.
Before the interval, Braintree began to threaten with two quickfire chances to open the scoring.
Matt Johnson first had a header cleared off the line before Ilic curled in a deep cross at the back post, which he then volleyed ferociously into the side-netting.
Immediately after the interval, Johnson denied Jackman’s effort from the edge of the area and then smothered Kayani following up to keep his side level.
The saves proved crucial as it kicked the hosts into gear as they started to dictate proceedings.
Crichlow was having more influence with his pace and trickery on the right, causing the Rebels defence to double up as he twice weaved his way into the box.
On 64 minutes, Braintree had strong appeals for a penalty as the ball pinged around the box and hit Lee Togwell, but the referee waved away the strong protests.
Holness had a growing influence as the game moved into the final 20 minutes, darting his way into the box causing North to be alert and stifle the attacker.
During the seven minutes of added time, Slough were unable to orchestrate a comeback and suffered their first defeat in four matches.
Braintree Town Line up
Billy Johnson, Matthew Maloney, Jay Porter, Matt Johnson (c), Kyran Clements, Luke Pennell, Gio Crichlow, Alfie Payne, Luke Holness (Dejon Noel-Williams 88), Kamil Conteh (Jean-Baptiste Fischer 56), Stefan Ilic (Jalen Jones 90+3). Unused substitutes: Wasiri Ola Williams, Michael Dome-Benwin.