Nelson opened the scoring from 25-yards just before half-time, which was followed by second half goals from Tobias Braney and an unfortunate Chris Francis own goal.
Despite a late consolation goal from the away side, courtesy of captain Ben Greenwood, Adrian Forbes' side continued their impressive start to the season and recorded their second win in succession at Kenilworth Road.
The young Hatters started well against their Premier League Cup opposition in front of over 350 Luton supporters and had the majority of chances to show for their initial dominance.
Nelson and Casey Pettit have both been involved in the first-team squad during recent matches and combined in the second minute to set-up the first chance of the match, but Pettit’s long-range drive was wide of the target.
Neat combination play was a consistent theme in Luton’s attacking play as Jayden Luker’s pass found its way to Conor Lawless, who helped the ball onwards to Josh Williams, but his first-time strike was comfortable for Billy Terrell to deal with in net for Bournemouth.
Nelson turned from chance creator to finding a shooting opportunity for himself a matter of moments later, but this time he fired over the bar.
Bournemouth winger Dom Sadi demonstrated his qualities driving forward in possession before flashing a shot just wide of the post.
Midway through the first half, Josh Allen was presented with a chance just outside the six yard box but spurned his effort from close range, forcing a strong save from Terrell.
Tobias Braney followed that effort 16 minutes later as he ran through on goal but the Bournemouth keeper was once again equal to it with a strong hand to turn it behind for a corner.
Terrell was no match for a Nelson free-kick, however, as the Development Squad broke the deadlock just before half-time.
After Allen was brought down on the left-hand-side, Nelson picked out the top corner from 25 yards leaving the goalkeeper helpless and consequently behind at the break.
Six minutes into the second half, the Development Squad had a golden opportunity to double their lead from the penalty spot after Allen was fouled in the area. The striker took responsibility from 12 yards but saw his first effort and rebound saved.
Fortunately a second goal was on the cards just six minutes later just after superb work from Matt Macey who produced a stunning double save to keep the away side out.
Braney received the ball from Nelson inside the area and with a touch onto his left foot rolled a low shot into the bottom corner.
The young Hatters' lead was extended further in unfortunate circumstances from a Bournemouth perspective. Allen put Chris Francis under presser in his own area and the defender's back pass went beyond Terrell and in.
The Cherries did reduce the deficit through captain Greenwood, who after receiving a switch from Emi Marcondes, cut onto his weaker right-foot and found the top corner.
The match was ended prematurely following a serious-looking injury to second half substitute Millar Matthews-Lewis, who was assisted off the pitch by club medical personnel and ambulance staff.
Development Squad: Macey; Jones (Pinnington 74'), Pettit (C), Tompkins, Williams; Lawless, Newton (Heron 80'), Luker, Nelson; Braney (Matthews-Lewis 64'), Allen (Lynch 80').
Subs not used: Bentley, Pinnington, Trialist.
Goals: Nelson (44'), Braney (58'), Francis og (66')
AFC Bournemouth U21: Terrell; Tonks (Trialist B 46'), Hill, Francis, Greenwood (C); Marcondes, Burgess (Daws 72'), Popoola; Boutin, Sadi; Pollock (Trialist A 61').
Subs not used: Camis, Okoh.
Goals: Greenwood (85')
