The Ryman League, Premier Division side started brightly and Jonathan Miles was forced to make three fine saves to keep it goalless in the first half.
However, Kingstonian played a slightly higher defensive line in the second half and we took advantage with runs from deep causing all sorts of problems.
That's how the deadlock was broken five minutes into the second half as the team went on to dominate the second half.
Barthram scored within 10 minutes of coming off the bench and although Kingstonian rallied late on, the final scoreline was about right.
Tim Sherwood set the team out in a 4-2-3-1 formation with John Bostock the lone striker and former Brighton defender Grant Hall alongside the impressive Milos Veljkovic in central defence.
Kingstonian had three chances inside the opening 10 minutes.
Dean Lodge struck the outside of the post with less than a minute on the clock and Miles then tipped Matt Pattison's free-kick around the post before a better save to deny Craig Mullen from six yards.
Cristian Ceballos, Ryan Mason and Alex Pritchard all tried their luck from distance and home goalkeeper Rob Tolfrey - a Spurs fan - did well to parry another clean hit from Pritchard from 20 yards.
Kingstonian hit back again and Mullen had a goal disallowed for offside before finding himself under a half-cleared cross six yards from goal, only for Miles to save with his feet.
Jordan Archer replaced Miles in goal for the second half and had considerably less to do as we dictated possession.
The opener arrived five minutes into the half as Tomislav Gomelt picked out Mason's run down the right channel. Mason drove into the box and drilled past Tolfrey at the near post.
Barthram entered the fray with Will Ekong and Jack Munns in the 58th minute as we started to carve out more chances.
Bostock fired just over from 20 yards and Barthram latched onto Mason's pass, cut inside Dominic Sterling and drove straight at Tolfrey.
Barthram could hardly miss when he found himself in front of goal again, as Kevin Stewart went into a challenge with Tolfrey and Sam Clayton and the ball ran into Barthram's path, six yards out and he tapped home for 2-0.
Kingstonian were handed a lifeline when Archer was judged to have brought down Clayton and Andre McCollin made no mistake from the penalty spot.
McCollin then had a golden chance to level but lashed wide from 10 yards three minutes from time.
Kingstonian (4-4-2): Tolfrey (Bragg, 75); Goode, Hutchinson, Murphy (Kamara, 44), Sterling; Pattison (Holloway, 46), Sankoh (Clayton, 46), Murray, Lodge; Mullen (Tait, 46), Small (McCollin, 46).
Spurs XI (4-2-3-1): Miles (Archer, 46); Byrne, Hall (Ekong, 68), Veljkovic, Stewart; Bentaleb, Gomelt; Pritchard (Barthram, 58), Mason, Ceballos (Munns, 58); Bostock.
Goals: Kingstonian - McCollin (penalty, 84). Spurs XI - Mason (50), Barthram (69).
Referee: Mr D Sheldrake.