The midfielder pounced after just 14 minutes to ensure victory against their illustrious opponents at Rush Green as he powered home a left-footed strike from outside the box.
West Ham featured the returning Paul McCallum as a lone frontman with Taylor Miles and Jordan Spence also handed starts as they looked to give some players game time during the break in Barclays Under-21 Premier League fixtures.
Town were on top for long periods of the first half though and almost took the lead on three minutes when Mark Cullen nodded over from a couple of yards out after a fine cross by Shaun Whalley.
McCallum had a similar chance just a minute later for Hammers when Sean Maguire’s cross was drilled across the box and just evaded the front man.
Luton took a deserved lead after 14 minutes though as captain Robinson’s effort flew into the bottom corner leaving Vit Nemrava with no chance.
There was little for either side to get excited about until three minutes before half-time when the Hammers had the ball in the net but McCallum was ruled offside when tapping home a Matthias Fanimo cross.
After the break, McCallum was denied again, this time seeing his header saved at point blank range by Elliot Justham after Sebastian Lletget had headed the ball into the box.
Town almost had a second with 20 minutes to go as Whalley cut in from the right flank, beating two players and striking a left foot shot which thumped the crossbar.
Substitute Blair Turgott made a difference when he was introduced but could garner nothing from several half chances as Luton were deserving winners.