Bricknell opened the scoring with a thunderous finish from close-range before Adeloye coolly tapped home Rory McAuley’s cross as Concord were rattled.
Aiden Palmer added to the lead with his deflected free-kick midway through the second-half with Bricknell netting his second of the game shortly after with a well-taken finish. Rangers made for a difficult end to the game, first with substitute Tony Stokes pulling one back with a finish from close-range before Steve Cawley added another three minutes after.
Adeloye calmed the nerves with six minutes of the game remaining when he curled a dazzling free-kick in the top corner to extinguish Concord’s hopes of further revival and extend City's unbeaten run to five matches.
Following Saturday’s 0-0 draw with Wealdstone, the Clarets made three changes with Marvel Ekpiteta, Tomi Adeloye and Harry Morgan all coming in for Mark Hughes, Moses Makasi and Hugo Skepelhorn.
Concord, now under the stewardship of Adam Flanagan following Danny Cowley’s move to Braintree, recorded a double over the Clarets last season, but City looked determined to overturn that with an attacking start to the game.
On Saturday though the Clarets never really got going in what was a frustrating match, but Mark Hawkes’s men looked up for the challenge and energised for the local derby with Luke Daley and Lee Sawyer looking to burst forward from the wide areas.
And it was those two who linked-up well, forcing Ben McNamara into his first save. Daley spread the ball wide, allowing Sawyer to take it in his stride before shooting low at the keeper, but the effort lacked any real conviction and was comfortably held.
But it didn’t take long for Concord to counter and after a mix-up in defence, Joe Gardner found space inside the area. He shifted on to his right foot to take Marvel Ekpiteta the wrong way, but the defender made amends after blocking the eventual effort on goal.
Rangers were then forced into some last-ditch defending of their own when an overhead kick inside the area was blocked before bedlam in-and-around the six-yard box eventually saw skipper James White hook clear from under his own crossbar.
Rory McAuley, who had the shot that was first saved by McNamara, featured in an unfamiliar role as a holding midfielder in place of Hughes, and looked a dominating figure.
Adeloye then had a good chance to put the hosts in front when he was one-on-one with the keeper, but he nicked it too far past the on-rushing goalie, committing a foul in the process.
Ex-Claret Max Cornhill initiated a promising move for the Beachboys, but it was soon ended by Christian Dibble’s strong save from George Doyle’s driven shot.
Dibble’s save was to prove even more crucial as Billy Bricknell put the Clarets ahead just shy of the half-hour mark. Adeloye pounced on a defensive slip to pull a save from McNamara, but the Clarets were rewarded when Luke Daley picked it up on the right to clip in a cross. Bricknell was at hand to thump home his fifth goal of the season and, more importantly, give the hosts a deserved lead.
Two minutes later the lead was doubled with Adeloye tapping home McAuley’s pin-point cross at the back post, his first goal in his first start for the side.
Concord looked shaken – they struggled defensively throughout the half and never cleared the ball with much conviction and were often on the back foot – but they had a chance to net a consolation, only for Steve Cawley to blaze over when he had time to pick his spot.
The Clarets, learning from their recent 2-2 draw with Havant which saw City’s 2-0 half-time lead slip, attacked with intent early in the second-half, almost capitalising on another defensive mix-up.
Keaton Wood slipped at the crucial moment, allowing Bricknell to pick the ball up and drive into the area. His cross found Daley in acres of space but the Clarets’ winger opted to take the chance first-time, firing disappointingly wide.
That miss almost proved crucial as Concord sensed blood and attacked with a little more purpose and vigour, but their work was almost undone by left-back Tom Stephen. The defender was left red-faced when his clearance towards his own goal dropped inches wide of the post with the ‘keeper rooted to the spot.
Chelmsford weren’t put off though and continued looking for a third. It came on 64 minutes after Daley was brought down by Cornhill. Aiden Palmer then stepped up to net his first in City colours since re-joining the club on-loan from Ebbsfleet, with the set-piece dropping into the far corner following a deflection.
Bricknell continued the scoring with a well-taken finish after cutting inside and dispatching past McNamara after finding himself with plenty of room.
Concord did, however, make for a nervy finish with substitute Tony Stokes netting from close-range two minutes later to give them some confidence.
And it did just that with Steve Cawley netting a second from inside the box as the Clarets looked a little disorganised in midfield and at the back.
Any glimmer of hope for Concord was dashed when Adeloye stepped-up to curl an incredible free-kick from 25-yards into the top corner for his second of the game.
That was enough for the Clarets to record the three points and extend their run to five games without defeat – promising form as the Clarets travel to Maidenhead on Saturday.
1. Christian Dibble
2. Mark Haines
3. Aiden Palmer
4. Marvel Ekpiteta
5. Marvin Ekpiteta
6. Rory McAuley (C)
7. Luke Daley
8. Lee Sawyer
9. Billy Bricknell
10. Tomi Adeloye
11. Harry Morgan
12. Hugo Skepelhorn (On for Billy Bricknell, 79’)
14. Bagasan Graham (On for Tomi Adeloye, 87’)
15. Laurence Vaughan
16. Amar Lewis
17. Connor Pearce
1. Ben McNamara
2. Luis Morrison
3. Tom Stephen
4. Max Cornhill
5. Arthur Lee
6. Keaton Wood
7. George Doyle
8. James White (C)
9. Joe Gardner
10. Steve Cawley
11. Lewis Taaffe
12. Jeremy Walker
14. Steve King
15. Bertie Brayley
16. Ben Greenhalgh (On for James White, 69’)
17. Tony Stokes (On for Lewis Taaffe, 69’)
Referee: Mr. Lee Venamore (Maidstone)
Assistant referees: Mr. Simon Finnigan and Mr. Leigh Crowhurst
Bookings: Chelmsford City: Mark Haines (4’, dissent), Lee Sawyer (43’, foul), Billy Bricknell (45’)
Concord Rangers: James White (58’, foul), Max Cornhill (64’, foul), Joe Gardner (80’) ,Tom Stephen (90')
Scorers: Chelmsford City: Billy Bricknell (29’, 73’), Tomi Adeloye (31’, 84’), Aiden Palmer (65’),
Concord Rangers: Tony Stokes (75’), Steve Cawley (78’)
HT score: 2-0
FT score: 5-2
City Man of the Match: Tomi Adeloye