Kildare had rallied from two goals down to trail 3-2 with eight minutes remaining of a highly entertaining contest remaining, before hat-trick hero Quinn collected the ball from Glory Nzinga's pass and rifled a terrific left foot shot into the bottom right corner of the net.
The goal finally broke Kildare's resistance as they had fought valiantly to claim the prestigious Under-14 inter-league title for a first time.
The DDSL's success is their third in successive years and their sixth in the last seven years.
The free-scoring Kennedy Cup winners managed 22 goals in their six games, conceding just three times.
Kildare made a dream start in the final when Jamie Duggan's free-kick was headed home by striker Dean Owens inside three minutes.
However, the DDSL drew level two minutes later when Quinn finished a rebound to the net from close range after Evan Ferguson's goal attempt was parried.
The pre-tournament favourites were in front in the 14th minute when Cherry Orchard's Craig King's cross was headed home superbly by Evan Ferguson, of St Kevin's Boys.
The DDSLs 2-1 half-time lead was quickly doubled when Ferguson turned provider for Quinn to grab his second of the game three minutes after the restart.
Battling Kildare, who recovered from losing their opening group game against Limerick County to reach the final, pulled a goal back with 10 minutes remaining when Owens, of Athy Town, scored his second with a superb volley, following excellent work from Matthew McCarrick.
However, the DDSL nerves were settled in the 52nd minute when Quinn completed his hat-trick, bringing his tally to four goals in two days, to help the competition's most successful side retain the Kennedy Cup.
Meanwhile, Donegal claimed third place in the 32-team tournament when easing past Cavan Monaghan 6-2 in their play-off.
Callum Gillen bagged a brace of goals for the winners, while Oisín Caulfield, Adam Carr, Luke McGlynn and Jamie O'Donnell were also on target.
Cork claimed a fifth-place finish when edging past Wexford 3-1 in the Plate final.
The Leesiders had two goals from Shane Tobin, of Corinthian Boys, while Harry Nevin, Douglas Hall, was also on the mark.
Results - Day 5 Kennedy Cup 2018
Kennedy Cup Trophy (25-26th places)
Drogheda 1-3 Galway
Shield Final (17th-18th places)
Limerick Desmond 0-0 NDSL (NDSL win 4-2 on pens aet)
Bowl Final
Kilkenny 1-0 Midlands (aet)
Plate Final (5th-6th place play-off)
Cork 3-1 Wexford
Third-Fourth place play-off
Cavan-Monaghan 2-6 Donegal
Kennedy Cup Final
DDSL 4-2 Kildare