Simmonds struck in both halves to give the Blue Square Bet South high-fliers a two-goal lead at Melbourne Park. And although Michael Rose pulled a goal back for the U's with a superbly-struck free-kick with 20 minutes remaining, Jamie Slabber wrapped up the hosts' shock victory late on.
Chelmsford took the lead when Simmonds netted from long range midway through the first half with a superb shot.
Colchester goalkeeper Mark Cousins then denied Justin Miller and although Jabo Ibehre went close for the npower League One side before half-time, the Clarets doubled their lead just after the hour when Simmonds nodded a long ball past the stranded Cousins and into the empty net.
Rose reduced the deficit with a 25-yard effort that left home keeper Stuart Searle motionless.
Colchester pushed for an equaliser after that and Magnus Okuonghae fired just over, while Searle made a fine save to deny Ibehre at his near post. But Slabber sealed Chelmsford's famous win in the closing stages when he slammed home from Simmonds' pass.