In an eventful encounter at Dagenham & Redbridge's Victoria Road, the 31-year-old midfielder opened the scoring in superb style after just 10 minutes when, positioned just inside Leicester's half, he volleyed the ball straight over the head of keeper Michael Price and into the net.
Hutch's goal of the season effort will live long in the memory of anyone who was in the stadium, but Hammers had other things to think about three minutes later, when 17-year-old defender Darren Blewitt was sent off for swearing at the linesman after being flagged for a debatable offside.
While many referees may have turned a blind eye to his outburst, the young left-back was no doubt guilty of using some 'industrial' language and left his team-mates facing a tough task to hang on to their lead.
Blewitt's dismissal forced Hammers to reshuffle, with under-17 coach Kevin Keen - playing his second reserve match of the season due to tomorrow night's FA Youth Cup tie against Norwich City restricting Roger Cross's selection - dropping to left-back and Richard Garcia asked to fight a lone battle up front.
Things went from bad to worse in the 24th minute, when Leicester striker Jon Stevenson was fouled in the penalty area by Izzie Iriekpen, and former Leeds United midfielder Matthew Jones tucked home the spot-kick.
Foxes midfielder Stefan Oakes then struck the crossbar with a looping shot and it seemed likely that the visitors would make their one man advantage pay.
However, inspired by the central midfield pairing of Hutchison and debutant David Noble - who protected the back four superbly all evening and also found the energy to get forward and support Garcia - the hosts fought back and were handed a glorious chance to restore their lead in the 31st minute.
A clever pass from Noble released Garcia in the box and the Australian striker was hauled back by a defender as he cut in on goal. Referee Singh immediately pointed to the spot, but Hutchison wasted the opportunity to double his tally, dragging his effort a yard wide of the target.
As with his wonder-goal, though, Hutch didn't have long to dwell on the incident, for Hammers did take the lead just two minutes later.
A slip by Leicester defender Tozer let in Garcia, who touched the ball past a defender and raced into the area before firing in a left-foot shot from an acute angle that squirmed under the dive of Price and into the bottom corner.
Hammers held on to their lead for the rest of the half, which included a five-minute period of injury timeâ€¦despite the fact that neither physio had been called on to the pitch!
When Iriekpen and French youngster Youssef Sofiane were forced off through injury at the interval, youth team prospects Ronnie Fletcher and Ayo Akinsete were handed their debuts at reserve team level, and with schoolboy midfielder Mark Noble included on the right of midfield, it didn't seem likely that Hammers would hold on for an entire 45 minutes.
Those who expected a claret and blue capitulation were in for a shock, though. With Garcia running himself into the ground up front - despite having missed a month of action due to a shin injury, Hutchison and the two young Nobles displaying a tireless determination in midfield and Raimond Van der Gouw providing a steadying influence behind a back four well marshalled by Gary Breen, the hosts restricted their opponents to just a handful of speculative efforts from outside the penalty area.
Indeed, it was Hammers who came closer to scoring, with Garcia flashing a fierce shot just over the bar and Akinsete - who gallantly played out the last 15 minutes with a hamstring injury after all three substitutes had been used - running through clear on goal but denied by a last-ditch tackle.
With just two minutes added on at the end of the second half, the wait for the final whistle wasn't too agonising. Hammers were able to celebrate a deserved and satisfying three points, while Hutch will no doubt remember his strike for a long time. And the good news is that the Sky TV cameras were there to capture it on film!
West Ham: Van der Gouw, Byrne, Blewitt, Breen,
Iriekpen (Fletcher 46), M Noble (McClenahan 74), Hutchison, D
Noble, Keen, Garcia, Sofiane (Akinsete 46). Subs unused: Jackson,
Leicester: Price, Mortimer, Ashton, Taggart, Tozer, Lewis (Deen 81), Jones, Reeves, Wright (Sutton 65), Stevenson, Oakes. Subs unsued: Murphy, Dawson, Powell.