The Clarets took the lead inside the first two minutes as Jeffers tapped in from close range after Mark Haines’ cross-come-shot flew across the six yard box.
It was to be the highlight of a far from vintage game of football with neither side creating little in the way of chances in the first half at least.
The second half started with a flurry with Michael Johnson making a brilliant double save to stop Haines and Jeffers from grabbing a second for the Clarets.
Former Claret Mason Spence forced Ross Fitzsimons into a low save and Matt Lench came close when he was found unmarked at the back post.
But in the end Jeffers’ 2nd minute goal was all that was needed as a second consecutive 1-0 home win saw Chelmsford go into Monday afternoon’s 2nd Round Draw.
A fortnight ago against Taunton Town the Clarets had to wait until the 89th minute to make the breakthrough as Anthony Church scored to send City in the 1st Round proper.
There was no need to wait that long this time around as Chelmsford made the ideal start to the tie by opening the scoring after just two minutes when Shaun Jeffers put the Clarets in front.
Max Porter was fouled by Callum Donnelly on the half way line with Chris Bush’s free kick into the box being smashed across goal by Mark Haines with Jeffers staying onside to tap home.
Having taken an early lead against a side from the division below you may have expected Chelmsford to kick on but their opponents began to grow into the game and created a handful of chances.
Ashley Miller was needed to head clear a vicious Kane Smith cross with Matt Lench ready to head home from close range. And Hitchin tried one off the training ground as Ben Walster’s low free kick into the box found Liam Brooks’ whose effort went just wide.
The Clarets came close to extending their lead when Elliott Buchanan’s placed effort was deflected millimetres wide with Michael Johnson wrong-footed, and the Canaries went straight up the other end and came close when Brooks cut onto his left to just miss the target once more.
For the rest of the first half it was pretty much a non-event with both sides cancelling each other out and not creating anything to threaten the games second goal.
That wasn’t to carry on in the second half though as Hitchin were indebted to their goalkeeper for keeping his side in the tie with a superb double save, first parrying Haines’ header from close range before stopping Jeffers' rebound.
A couple of minutes later and Haines had an even better headed chance come his way as Robbie Willmott’s corner found the City centre half completely unmarked eight-yards out but he somehow managed to send his header over.
Hitchin caused a goalmouth scramble when a header across goal looked like it was going to be tapped in at the far post by Lench, but after the midfielder failed to convert eventually it was cleared by the Clarets after a number of blocked shots.
The Clarets thought they should have had a penalty when a short back pass was latched onto by Jeffers who went down after Johnson came flying off his line to try and clear, but the referee was having none of it and booked the City striker for diving.
After a flurry of early chances for both sides the second half began to mirror that of the first and was not one for any neutrals in amongst the 469 in attendance.
Hitchin began to apply some pressure late on and a quickly worked corner almost caught City out as Lench was found unmarked but his shot was cleared off the line by Miller.
From the resulting corner Brooks had a header on target hacked away and in the final minute of six minutes added on Chelmsford dealt with a late free kick into the box, seeing it out for a goal kick as the Clarets held on to make the 2nd Round for the first time in in four years.
17. Ross Fitzsimons
2. Ashley Miller
3. Bagasan Graham
4. Max Porter
5. Chris Bush (C)
6. Mark Haines
7. Robbie Willmott
8. Josh Rees
9. Shaun Jeffers
10. Elliott Buchanan
11. Jake Reid
12. Phil Walsh
14. Luke Daley (On for Jake Reid 69’)
15. Max Cornhill
16. Frankie Merrifield
18. Matt Young
1. Michael Johnson
2. Kane Smith
3. Ben Walster
4. Josh Bickerstaff
5. Dan Webb (c)
6. Lewis Rolfe
7. Matt Lench
8. Callum Donnelly
9. Michael King
10. Liam Brooks
11. Lucas Kirkpatrick
12. Will Wright (On for Lucas Kirkpatrick 87’)
13. Will Hunt
14. Mason Spence (On for Michael King 56’)
15. Conor Clarke
Chelmsford City: Shaun Jeffers 2’
Hitchin Town: None
Chelmsford City: Ashley Miller 62’, Chris Bush 68’, Shaun Jeffers 70’
Hitchin Town: Kane Smith 40’, Callum Donnelly 45’, Matt Lench 58’
Referee: Josh Smith
Assistant Referees: Michael Smith & Ahmad Rafique
City Man of the Match: Josh Rees