The Irish full-back hit a screamer into the top corner from fully 30 yards to put us in control at 2-0 in the 75th minute. Calum Davenport wrapped up the three points from the penalty spot two minutes later.
Clive Allen's starting line-up included four Academy players - Jamie Davis, Jacques Maghoma, Stuart Lewis and Andy Barcham - as well as the relative youth of Charlie Lee and Charlie Daniels. Joe Martin came on at the start of the second half and the late arrivals off the bench of Simon Dawkins and Alex Smith made it seven Academy lads on show.
They all impressed in what must rank as one of the best performances and certainly results of the season to maintain top spot in the Barclays Premier Reserve League South.
Charlton arrived at Stevenage fourth in the table and with the big guns up front - Jason Euell, Jay Bothroyd and Kevin Lisbie all started, backed-up by Darren Ambrose in midfield.
Lee and Davenport stood up to the task, however, and Radek Cerny as always produced the saves when called upon - the pick a superb reaction stop to deny Ambrose in the first half.
It was an all-action first half and we only had to wait 14 minutes for a fine opening goal as Davis played the ball wide to Daniels who strode inside Wilson before firing into the far corner across Anderson.
It was the perfect start after Ambrose had threatened early on and the Premiership regular was at it again soon after, showing lightning pace to burst into the box only for Kieran McKenna to halt him in his tracks with the perfect tackle.
Ambrose then provided the pass for a Bothroyd effort on goal and the midfielder was on hand again to guide the ball goalwards from close range after 37 minutes only for Cerny to keep it out with a superb reaction save.
Clive, who opted for a 4-5-1 system, reshuffled at half-time with McKenna off, Martin on and Jackson moving to left-back.
The lads refused to allow Charlton to settle at any stage and Ambrose's contribution started to fade - Bothroyd the more likely threat for the visitors in the second half and that only via shots from distance.
Jackson, so impressive again, saw his cross-shot tipped onto the top of the crossbar by Anderson just after the hour mark as both sides looked for the match's crucial second goal.
When it arrived, it was worthy of winning any match on any stage. Lewis laid the ball square to Kelly supporting from right-back, he controlled, took a couple of steps forward and unleashed an unstoppable shot into the top corner from fully 30 yards.
Two minutes later and it was all over as the hard-working Barcham went over in the box and Davenport buried from the penalty spot.
GUIDE TO THE ACTION...
3mins: Ball over the top almost caught Cerny out, keeper dashed out of box to head clear but it bounced over him, McKenna back to clear.
4mins: Ball loose in box, Davis didn't get enough on shot to trouble Anderson.
6mins: Jackson free-kick from 20 yards clipped side-netting with Anderson rooted to spot.
11mins: Ambrose and Lisbie combined down left, Ambrose into box, dragged shot across face of goal.
14mins: GOAL. Davis played wide to Daniels on left, he ran at Wilson before unleashing drive from 20 yards that flashed across Anderson into far corner. 1-0.
18mins: Half-chance fell to John when corner was only half-cleared, sliced shot over.
20mins: Davenport inches away from Jackson's inswinging corner.
21mins: Ambrose lightning pace down left took him into box, looked to cut inside McKenna to open up shooting chance but McKenna made textbook tackle to deny him.
23mins: Ambrose reverse pass released Bothroyd, difficult angle, Cerny comfortable save.
33mins: Jackson and McKenna threw themselves in to block Bothroyd's piledriver.
37mins: Cerny brilliant reactions to turn aside Ambrose's effort from close range, Lee then on hand to block John's follow up.
39mins: Barcham quick turn and away in a flash, carried 10 yards before hitting a shot that bounced awkwardly in front of Anderson who did well to turn around post.
Added time: Bothroyd plenty of whip and curl on free-kick 25 yards out, Cerny read it and parried but was on his toes to grab rebound.
Half-time: Spurs 1, Charlton 0
47mins: Good move, Kelly low cross from right met by Davis, first-time volley zipped just over.
56mins: Another sweetly-struck Bothroyd free-kick flicked off Lewis but Cerny saw all the way and made smart low save.
63mins: WOODWORK. Great break from Charlton attack, Lewis carried out of defence and fed Jackson on left, his cross-shot tipped onto the top of the crossbar by Anderson.
75mins: GOAL. Lewis played square to Kelly who steadied himself and smashed into the top corner from 30 yards. 2-0.
77mins: PENALTY. Looked a harsh one on Youga, who appeared to block tackle Barcham in box, penalty awarded and stroked home by Davenport. 3-0.
86mins: Bothroyd whistled a drive just wide from 20 yards.
Full-time: Spurs 3, Charlton 0
Spurs: Cerny, McKenna (Martin, 46), Kelly, Lewis, Lee, Davenport, Davis (Smith, 87), Jackson, Barcham, Maghoma, Daniels (Dawkins, 72). Unused subs: Burch, Kyriacou.
Charlton: Anderson, Wilson, Ashton, Phillips, Youga, Sankofa, John, Ambrose, Lisbie, Euell (Weston, 74), Bothroyd. Subs: Walker, Woolley, Brandao, Yussuff.
Stephen Kelly struck a wonder goal as our young reserve team passed the test against Charlton with flying colours on Monday night.