The Heed handed themselves the initiative after just nine minutes as Michael Nelson headed into the bottom corner for his first Gateshead goal.
Kayode doubled the lead from close range after withstanding Brackley pressure early in the second period to secure a first win of the season at the GIS.
Mike Williamson made just one change to the side that drew 1-1 at York City on Bank Holiday Monday, dropping himself due to injury and bringing Nelson into the middle of defence.
The hosts started on the front foot at the International Stadium, getting on the ball and looking to force the issue as soon as possible.
Force the issue they did after nine minutes when Nicky Deverdics’ free-kick into the centre of the box was headed into the bottom-right corner by Nelson, who found himself unmarked in the box.
JJ O’Donnell had the opportunity to put the Heed two goals to the good four minutes later as he beat the offside trap on the left-wing, but saw his effort saved by Danny Lewis as he tried to sneak the ball into the far corner.
The game’s pace depleted somewhat shortly afterwards however with neither side able to create a chance on goal until just before the half-hour mark.
Shane Byrne’s 25-yard free-kick for the Saints was parried to the far-post by Brad James, where Matt Lowe failed to re-direct the ball goalwards before the offside flag was raised.
James had to stay alert to keep Thierry Audel from getting his name on the scoresheet a few minutes later as the Boro loanee pulled off an impressive to hold the Brackley man’s strike while diving towards the far post.
The Saints had two opportunities to haul themselves level early on, firstly through Lee Ndlovu who saw his shot from inside the area well saved by James, before Jimmy Armson fired wide on the turn following a scramble in the penalty area.
Their profligacy proved costly moments later as Kayode doubled Gateshead’s lead from close-range after Elliot Forbes picked up Audel’s clearance, before the midfielder played into the middle for the Rotherham loanee to tap home.
Greg Olley and Deverdics both sent effort just clear of goal as the Heed looked to make it 3-0, the former firing over from 30 yards while the latter curled just wide from inside the area.
It made no difference to the final result however, with Gateshead securing their second win of the season by a two-goal margin.
Gateshead XI: James; Nicholson, Lees, Nelson, Barrow (c); Oliver (Forbes, 18’), Agnew; Olley, Deverdics, O’Donnell (Tear, 87’); Kayode (Blackett, 90’).
Unused subs: Guthrie, Greenfield.
Goals: Nelson (9’), Kayode (63’)
Bookings: Agnew (40’), Nicholson (60’)
Brackley Town XI: Lewis; Myles (Holman, 86’), Walker, Byrne, Audel, Dean (c), Lowe (Fairlamb, 69’), Armson, Ndlovu, Baker (Daire, 69’), Murombedzi.
Unused subs: Franklin, Langmead.
Bookings: Audel (20’), Byrne (54’), Walker (60’)
Referee: Andy Sykes
MOTM: Joshua Kayode