Knowles took his goals tally to an incredible nine in three home games at the CNG Stadium with two first-half strikes - the first from the spot and the second from close range.
Gloss arrived in the second period with a fine team goal to seal victory 19 minutes from time, with National League North player of the season Leesley clinically netting from close range.
It was the prelude to party time for delirious home supporters at a sun-drenched Wetherby Road as Town clinched promotion in champagne fashion amid regular chants of ‘Town are going up.’
It represented the perfect end to the campaign for long-serving manager Simon Weaver, with the club’s Holy Grail of Conference football now a joyous reality.
An eventful first-half saw Harrogate make the all-important breakthrough, courtesy of an ice-cool 26th-minute penalty from in-form Knowles.
Referee Leigh Doughty pointed to the spot after Brackley defender Alex Gudger was adjudged to have blocked Leesley’s goalbound strike with his arm and Knowles proceeded to send visiting keeper Danny Lewis the wrong way with his confident penalty.
Nine minutes later, the predatory striker spurned a golden chance to notch his second when he wastefully fired wide after profiting from a defensive misdemeanour from Brackley and racing clear.
But the home marksman shrugged off that miss to showcase his clinical streak to double Town’s tally five minutes before the break.
A free-kick from Leesley was not cleared and Knowles reacted quickest to splendidly hook the ball home in instinctive fashion from close range.
While Knowles extended his recent purple patch on the goalscoring front, his opposite number Aaron Williams did not fare so well, with the prolific 36-goal striker denied by a fine reaction save from Town keeper James Belshaw shortly after Harrogate’s opener and glancing a header inches wide just before the hosts’ second.
George Thomson saw a low shot fly just wide early on, but it was Brackley who displayed the early conviction with Town rocked by the early departure of big striker Mark Beck, stretchered off with a leg injury after coming off second best in a challenge with visiting captain Gareth Dean.
Town captain Josh Falkingham did well to get in the way of a goalbound shot from Shane Byrne and then made an even more telling intervention, clearing a point-blank header from Gudger off the line following a Brackley corner.
It proved key with Knowles firing the hosts in front just over five minutes later and after his uncharacteristic miss, normal service was resumed with a second for the hosts, who suffered a second untimely blow just before the break when substitute Jake Wright became the second Harrogate player to be stretchered off with an injury after colliding with Dean.
Brackley’s profligate finishing traits also resurfaced on the restart, with Lee Ndlovu being the guilty party after racing clear, but with only keeper Belshaw to beat, the forward inexplicably lobbed the ball over.
At the other end, Town almost grabbed a game-sealing third with Leesley’s left-wing cross picking out Thomson at the far post, but his angled shot was blocked by Lewis.
A goalmouth scramble then saw Brackley also profit, with Jimmy Armson just failing to convert as the visitors desperately sought a lifeline to get back into proceedings.
Pressure was sustained from the Saints, but they could not find a way through.
A lovely team goal then made the game safe for Town with Leesley finishing off an excellent low cross from Ryan Fallowfield on 71 minutes.
An audacious Lloyd Kerry lob almost added a fourth for the hosts and Joe Emmett struck the post after racing away, but three goals proved plenty on a historic afternoon for Harrogate as the Saints were left to focus on their forthcoming Trophy final with Bromley.
Harrogate Town: Belshaw; Fallowfield, McCombe, Burrell, Parker, Thomson, Emmett (Agnew 90), Falkingham, Leesley; Knowles, Beck (Wright 12 (Kerry 45)). Substitutes unused: Cracknell, Kitching.
Brackley Town: Lewis; Murombedzi, Dean, Gudger (Myles 84), Franklin; G Walker, A Walker (Lowe 58), Byrne, Armson, Ndlovu (Brown 66), Williams. Substitutes unused: Graham, Iaciofano.
Referee: L Doughty.