The Clarets edged the Fourth Qualifying Round replay 1-0 on Monday night at the Melbourne Stadium against National League South rivals Bath City.
As in Saturday`s original tie which finished goalless at Twerton Park, there was little to choose between the teams throughout the match, although the strong gusting wind was making things difficult for both sides.
Bath came close to opening the scoring when Craig Braham-Barrett almost put through his own net before Jack Compton fired wide at the other end.
Nat Jarvis saw his header saveed by Clarets `keeper Sam Beasant and Andy Watkins missed a great chance to put Bath in front right on half-time.
However, 5 minutes after the break, Michael West scored the first goal in the tie from a Danny Green cross to give Chelmsford the lead.
Bath threw everything forward late on in an effort to force an equaliser, but Chelmsford held firm.