The visitors had made the most of fine conditions at Old Northamptonians to score first, but the Saints looked to have the game wrapped up even before the half hour with a try-bonus provided by Sam Harry, Josh Skelcey, Simon Uzokwe and Reece Marshall.
Leeds rallied admirably after the break, however, scoring twice with Marshall in the bin but back to a full complement having had their lead cut to a solitary point, the Saints again thrust clear in a killer final five minutes.
If those last five were impressive though, their first five were not and Leeds took full advantage of the slow start - Nick Rawsthorne cutting gaps in the home defence to score with just 2 minutes gone.
The travellers kept the squeeze on too, but after Sam Olver cleared the Saints' lines, Lewis Hall and Steve Arroyo-Hover combined with some smart offloading to catch Leeds off guard and send Sam Harry over.
The score proved a real shift in momentum and when Skelcey was first to a Saints chip through, the Academy's leading try scorer also had the strength to outmuscle opposite number Rob Rekis for his seventh of a prolific season.
The wing played a key part in the build-up to the third try, too, Leeds again struggling to deal with his blistering pace that took his side to within 10 metres, where Uzokwe compounded the good work, the prop tapping a quick free-kick and darting beneath Leeds' posts.
By now it was all Saints and another try would come five minutes before half-time through skipper Marshall's unstoppable burst. Although Leeds reacted with their second just moments later, the Saints went into half time 26-10 up and in control.
Leeds started the second half the way they finished the first with plenty of pressure and while it wouldn't immediately yield points, it would see Marshall sent to the bin on 42. With a penalty shortly before the bin and a try during, Leeds took full advantage and sizeable Saints lead was now looking increasingly fragile.
Scrum-half Sam Gaudie set further alarm bells ringing when he crossed for Leeds' bonus score to make it 26-25 but as impressive as the Leeds comeback was, the way the Saints youngsters handled it was even better.
Having protected their now slender lead and reassumed the upper hand, Saints' limitless hard work paid off as they finally killed off a yoyo battle.
Replacement back row Harry Betts was first to benefit, taken over by a driving maul, and in the dying seconds Alex Wootton cut the Leeds defence to shreds and coasted in on the right to seal his side's first victory in the newly formed Academies League.
Having seen the tie switch venues relatively late on, Saints' Dusty Hare voiced the club's appreciation for Old Northamptonian's hospitality.
"We would like to extend a big thank you to ONs for allowing us to play this game at such short notice," he said. "The facilities at the club are very good and the club gave us first class hospitality.
"Saturday's game certainly showed the value and opportunity of using these games to connect with local clubs in our region."
2mins LEEDS Try Rawsthorne 0-5
9mins SAINTS Try Harry Con Olver 7-5
14mins SAINTS Try Skelcey 12-5
21mins SAINTS Try Uzokwe Con Olver 19-5
30mins SAINTS Try Marshall Con Olver 26-5
35mins LEEDS Try Armstrong 26-10
HALF-TIME SAINTS 26 LEEDS 10
41mins LEEDS Pen Rawsthorne 26-13
46mins LEEDS Try Witty Con Rawsthorne 26-20
56mins LEEDS Try Gaudie 26-25
65mins SAINTS Try Betts Con Olver 33-25
70mins SAINTS Try Wootton Con Olver 40-25
FULL-TIME SAINTS 40 LEEDS 25