Dave Carter's side conceded twice inÂ stoppage-time at Dover Road, having been on their way to an impressive victory.
Moneys took the lead after 13 minutes. Conor Bailey's cross from deep picked out Joe Briggs inside the box and he crashed a first-time volley over the visiting keeper's head.
The hostsÂ doubled their advantage midway through the second half.
FelipeÂ Barcelos and Hutchings combined inside the boxÂ before the former was brought down to win his side a penalty.
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The Moneyfields captain stepped upÂ and emphatically sent the spot-kick into the net.
Hutchings looked to have wrapped up a win for the hostsÂ in the 72ndÂ minute with a brilliant effort.
The former Hawks forward received the ball from Barcelo 35 yards from goal before catching the Melksham keeper off his line by dinking a shot over his head.
Yet Melksham refused to be beatenÂ and left Moneys shell-shocked.
They grabbed a goal back with eight minutes remaining before scoring twice in added-time to snatch a point.Â
Meanwhile, in the Wessex League premier division, second-placed Horndean openedÂ a four-point advantageÂ over AFC Portchester with a 4-2Â derby win at the Crest Finance Stadium.
Michael Birmingham's Deans broke the deadlock in the 32ndÂ minute when a Royals defender put a cross into his own net.
The home side equalised just a minute after the start of the second half.
Alfie Lis regained Horndean's advantage in the 79thÂ minute.
There was late drama with three goals being scored in the dying embers.
Harry Jackson netted a third for the visitors with a minute of normal time remaining, before swiftly grabbing a second.
Portchester scored a consolation but lost ground on the Deans in the race for promotion.Â
Baffins claimed a derby success with a 3-1 defeat ofÂ Fareham Town at the PMC Stadium.
Bognor needed penalties at Nyewood LaneÂ to move into the next round of the FA Trophy.
The Rocks claimed a 3-2 shoot-out victory over Bracknell Town, after the game had finished 2-2 following extra-time.