Kenny McEvoy, Jon Obika, Simon Dawkins and Cristian Ceballos were on target at Kingsmeadow.
Chances were created at regular intervals as the lads quickly snapped back into rhythm against the Ryman League Premier Division side.
Ceballos, playing off the right of the front three, went close inside five minutes and we were soon in front.
McEvoy led a break from deep, rolled the ball wide to Obika and continued his run into the box. Obika showed strength to hold off Marcus Moody and when he clipped the ball into the box, McEvoy darted between defenders to head home.
Obika was there again to double the lead on 20 minutes. Giancarlo Gallifuoco provided the pass this time and Obika, again left of centre, cut onto his right foot and took aim, the ball clipping off Matt Drage and looping home.
Gallifuoco stung Rob Tolfrey's fingers from distance and Ceballos looked set to turn home McEvoy's cross, only for his effort to clip off Moody and divert just wide.
The final chance fell to Obika, who dragged his effort just wide of the far post.
The management team made four changes at the break, introducing Jonathan Miles in goal, Shaq Coulthirst, Laste Dombaxe and Academy Second Year Aaron McEneff.
Tolfrey did well to block a blaster from Ceballos in the 55th minute and it didn't take long for us to claim a third goal.
Dombaxe and Coulthirst were both involved before Adam Smith darted into the box and laid off for Simon Dawkins, who fired low across Tolfrey and into the far corner.
Ryan Moss fired over as Kingstonian looked for a response, but play was soon down the other end as first Ceballos and then McEneff were just off target from 25 yards.
Kingstonian came closest in the 77th minute, when Page met Kavanagh's corner and Moss nodded the second ball just over under pressure from Miles.
Ceballos and Roman Michael-Percil went close in the final stages and the last word went to Ceballos in the 90th minute.
Ryan Fredericks backheeled the ball to the Spanish winger on the right of the box and he lashed in a drive that flew between Bashiro Alimi and Coulthirst to leave substitute goalkeeper Billy Henshaw helpless.
Kingstonian (4-4-2): Tolfrey (Henshaw, 77); Goode (Ofusu-Hene, 46), Drage (Sampayo, 46), Page (Alimi, 46), Moody; Pattison (Jelley, 46), Sweeney, Kavanagh, Okojie; McCollin (Somner, 46), Moss.
Spurs XI (4-3-3): Archer (Miles, 46); Fredericks, Ball, Stewart (D McQueen, 65), Smith; Dawkins (Michael-Percil, 60), Gallifuoco (A McQueen, 61), Lameiras (McEneff, 46); Ceballos, Obika (Coulthirst, 46), McEvoy (Dombaxe, 46).
Goals: Spurs XI - McEvoy (7), Obika (20), Dawkins (58), Ceballos (90).
Referee: Mr D Sheldrake.