Ever-enthusiastic Poyet - on hand to throw himself in the way of a West Ham chance in injury time - bagged the equaliser and set up the winner as he completed a 90-minute shift while Ziege appeared untroubled in 73 minutes of action.
Stephane Dalmat was the inspiration though for this first win of the FA Premier Reserve League campaign.
The fleet-footed Frenchman played a huge hand in both goals, grabbing the second himself, as Colin Calderwood's men recovered from Richard Garcia's stunning effort to bag maximum points.
The first half was neat and tidy from both sides as we edged possession without really creating clear-cut chances.
The action arrived in patches with three efforts inside the opening two minutes - Garcia's effort drifting a yard wide, Dalmat showing his skills before shooting straight at Bywater and Poyet clipping the top of the crossbar from Ziege's cutback.
Jackson was the driving force in midfield and his low drive, deflected wide, was the next effort of note after 20 minutes before Dalmat's snapshot was plucked out of the top corner by Bywater seconds later.
It was Jackson again after 35 minutes as he bulldozed through a 50-50, played a one-two with Poyet only to drag his shot wide.
But it was West Ham, whose threat had been negligible, who took the lead just before the break. It was a cracking goal as well, out of nothing, as Garcia controlled, worked a yard of space and smashed the ball home off the inside of the post from 25 yards. Unstoppable.
Bywater was there again to deny Jackson at his near post minutes into the second half only for Burch to match him at the other end as Byrne raced clear one-on-one.
The turning point of the game arrived just after the hour. Byrne poked wide a great chance for Hammers to double the lead and within a minute, we were level.
Dalmat injected a yard of pace, sped into the box and squared for Poyet to clip home from 10 yards.
Five minutes later and Dalmat repeated the trick, bursting out of the blocks, playing a one-two with Poyet and finishing with style for 2-1.
There were few chances after that - the industrious Blondel dragged his shot wide and Poyet was there to block as Noble had the last chance of the night in injury time.
MINUTE BY MINUTE
30secs: Garcia jinked away from Doherty, shot drifted a yard wide.
1min: Dalmat flicked ball over Kilgallon, dipping shot comfortable for Bywater.
2mins: WOODWORK. Ziege played in down the left side, clever cut back to Poyet in space 10 yards out, shot clipped top of the crossbar.
20mins: Jackson drive after Dalmat run looked promising until deflected wide.
21mins: Dalmat snapshot plucked out of top corner by Bywater.
35mins: Jackson won 50-50 cruncher in midfield, one-two with Poyet, dragged shot wide.
42mins: GOAL. Garcia scorcher out of nowhere, in off inside of left post from 25 yards. 0-1.
Half-time: Spurs Reserves 0-1 West Ham
48mins: Jackson onto Poyet flick, shot blocked by Bywater.
52mins: Noble slipped ball through to Byrne, clean through one-on-one, Burch came out on top to block with legs.
62mins: McMahon pass into Byrne, Burch out quick, toe-poked wide.
63mins: GOAL. Dalmat injected a yard of pace, into the box, squared for Poyet to clip home from eight yards. 1-1.
67mins: GOAL. Another Dalmat burst out of the blocks, one-two with Poyet, made no mistake from close range. 2-1.
82mins: Blondel dragged shot wide from close range.
Injury time: Poyet there to block good chance for Noble.
Line-ups: Spurs: Burch, Marney (Hughes, 53), Ziege (Galbraith, 73), Kelly, Mabizela, Doherty, Dalmat, Blondel, Jackson, Poyet, Barnard (Slabber, 74). Unused subs: Eyre, Henry.
West Ham: Bywater, McClenahan, Tattam, Laws, Lumsden, Kilgallon (Blewitt, 45), Sofaine, Byrne, Garcia, Noble, McMahon. Unused sbs: Behcet, Pearson, Cohen, Noble, G Carrick.
Goalscorer Gus Poyet and Christian Ziege completed successful returns as our reserves got off the mark against West Ham on Monday night.