Harriers now have 13 points from their six games with four wins and a draw and sit seven points off leaders Gloucester City, albeit with two games in hand.
The visitors were ahead early on when Amari Morgan-Smith fired home after five minutes.
The striker was in perfect position to convert from close range after a fine cross from defender Alex Penny.
Brackley showed they were up for the battle though and had a couple of efforts on the Harriers’ goal without finding the net.
And they were made to pay just after the half-hour when Harriers doubled their lead.
Omari Sterling burst forward and made the most of the time and space on offer to lay off to full-back Caleb Richards, and his cross was met Sam Austin to put Harriers two up.
Brackley almost struck back ten minutes into the second half when Lee Ndlovu fired an effort against the woodwork.
From then on, Brackley laid siege to Harriers’ goal but the visitors put bodies on the line to take the three points.