The home side took the lead on seven minutes, Noble scoring from a free header.
Tom Hill equalised before the break, slotting home following good work from Steve Callinan.
In the second period the Ducks took the lead. Hill scoring his second of the evening, firing home after Braintree failed to clear.
But the Essex side were level after just three minutes when Reinelt headed in from close range.
Disaster struck with just eight minutes on the clock when Mark Jones fired an unstoppable volley past James Courtnage.
A more heartening display, but Aylesbury still left Cressing Road empty handed.