The Urchins took the lead on fourteen minutes as Charlie Stimson rounded McDonald and poked home from a tight angle.
The visitors held on until half-time having limited City to very few chances during the first half.
Rhys Murphy levelled for Chelmsford with an excellent low volley before Adrian Cascaval headed beyond Callum Chafer to score his first goal for the Club.
Jonny Giles capitalised on poor marking to seal progression to the final by arrowing a shot into the top corner.
The Clarets will take on either Billericay Town or East Thurrock United at the JobServe Community Stadium on Tuesday 9 April.