Buchanan opened the scoring on 50 minutes as he diverted Robbie Willmott’s cross beyond Matt Rice with a stinging volley. Jeffers completed the victory with ten minutes left as he saw his shot loop over Rice, taking a deflection from Arran Pugh on its way.
Both sides started the tie slowly, but the hosts had the first chance of the half when Willmott saw his effort from a tight angle deflected out.
The next opportunity fell to the visitors, but a superbly-timed challenge from Mark Haines made sure that Niall Thompson could not supply a cross.
Truro were quick back into action as Thompson was involved again. The speedy striker beat the offside trap to follow a long-ball, but his lobbed effort went wide after Fitzsimons was spotted off his line.
A tactical change in shape invigorated the hosts and allowed them to tuck behind the defenders, a change that proved to affect the outcome of the League clash.
The adjustment in style showed its effect when the Clarets should have broken the deadlock. Buchanan’s driven cross smacked into Jeffers - who had plenty of space at the far post – but the ball dropped just wide of the upright.
Chelmsford had loud claims for a penalty waved away when Mark Haines’ low driven effort hit against the post before Jeffers was bundled over inside the area.
Thomspon became the first entrant to referee’s book when he was shown a yellow card after bringing an end to Jeffers’ darting run.
The Clarets started the second half in opposite fashion to the first, and their quick start quickly troubled the visitors but Anthony Church’s rapid cross evaded Jeffers.
But the home side’s earlier miss did not matter as quickly after Buchanan sent a sweetly struck volley past Rice grabbing his fifth goal of the season.
The City striker almost added a second to his tally as he darted between two Truro defenders, but his final product was a waste as he dragged his effort wide.
The visitors had a golden chance to equalise when Thompson squeezed his way into space on the by-line, however his final touch knocked the ball out of play.
The fast-paced action continued in the final quarter of the game when Thompson drilled a cross past Fitzsimons but no-one could tap it home.
But the result was in no doubt as Shaun Jeffers’ shot ricocheted off Pugh before beating Rice on 80 minutes.
The visitors were unable to net a mere consolation goal and the Clarets go into Saturday’s FA Trophy game at Tranmere Rovers in the best possible fashion.
1. Ross Fitzsimons
2. Ashley Miller
3. Daniel Blanchett (69’ Bagasan Graham)
4. Josh Rees
5. Michael Spillane
6. Mark Haines
7. Robbie Willmott
8. Anthony Church © (86’ Max Porter)
9. Shaun Jeffers
10. Elliott Buchanan
11. Kane Haysman (77’ Max Cornhill)
12. Chris Dickson
14. Max Cornhill
15. Josh Porter
16. Bagasan Graham
17. Max Porter
1. Martin Rice
2. Ben Adelsbury
3. Jamie Richards
4. Ollie Knowles (73’ Tyler Harvey)
5. Aaron Bentley
6. Arran Pugh ©
7. Zane Sole
8. Niall Thompson
9. Andrew Neal
10. Dan Smith (62’ Ryan Brett)
11. River Allen
12. Charlie Duke
14. Tyler Harvey
15. Les Afful
16. Fletcher Williams
17. Ryan Brett
Yellow Cards: [b]
Chelmsford City: None.
Truro City: Niall Thompson (42’).
[b] Goalscorers: [b]
Chelmsford City: Elliott Buchanan (50’), Shaun Jeffers (80’).
[b] Attendance: 925.
City Man of the Match: Elliott Buchanan.
Referee: Gary Parsons