The young striker pounced from close range at the end of the first half to add his first reserve goal to his first FA Youth Cup strike last Thursday.
But the Hammers took the spoils via the impressive Richard Garcia's twice-taken penalty in the second half - the same player had earlier opened the scoring with a thunderous shot into the top corner.
After a scrappy start the first half burst into life with two goals in two minutes.
The visitors took the lead with a magnificent strike out of nothing from Garcia, who latched onto Cisse's pass before smashing a shot from the right corner of the box across Sullivan into the top-left corner.
It only took two minutes for Colin Calderwood's men to respond. Ricketts battled his way past Blewitt before squaring for Malcolm to slide home from close range.
There was little to report before the goals.
Sullivan made the only save of the half after four minutes, a decent stop to his left from Cisse's low strike, Garcia's burst into the box was halted by the excellent Thelwell on the half-hour and Ricketts appeared caught between a cross and shot after good work from the industrious Galbraith after 38 minutes.
The second half started brighter for Spurs and Ricketts was unlucky to see his volley clip the post with Van der Gouw beaten after Galbraith robbed Delaney and picked the midfielder out.
But it was West Ham who grabbed the advantage again after 67 minutes.
Garcia again made something out of nothing, intercepting a loose pass on the centre circle before taking off on a dribble into the box and flicking the ball to Byrne, who was upended by Jackson.
Garcia slid the penalty home only for the referee to order a re-take - the same player made no mistake second time around, hammering it into the roof of the net for 2-1.
We probed away with little reward in terms of chances until the 87th minute when substitute Mark Hughes' dipping volley forced Van Der Gouw into a scrambling save at the foot of his post.
Line-ups: Spurs: Sullivan, Henry (Hughes, 45), Thelwell, Thatcher (Foster, 81), Bowditch, Freund, Toda, Galbraith, Ricketts, Malcolm. Subs: Yeates, G Kelly, McKie.
West Ham: Van der Gouw, A Ferdinand, Blewitt, Cisse, Delaney, Ward, Lumsden, Byrne, Garcia, Pearson (M Cole, 81), McMahon. Subs: B Forde, D Forde, Laws, G Carrick.
Michael Malcolm's second goal in a week wasn't enough as the reserves slipped to defeat against West Ham at Stevenage Borough on Tuesday night.