Louie Theophanous sent the travelling Chelmsford supporters into delirious scenes as he powered a header with twenty minutes left.
But Chris Dickson sealed the victory with five minutes left as he drove forward from forty-odd-yards before striking beyond Ibrahim.
Duane Ofoi-Acheampong scored a late consolation goal for the hosts but it was too little too late as the Clarets won for the third time at Princes Road this season.
City boss Rod Stringer made two changes to the side that drew 0-0 in the first leg at The Melbourne Community Stadium on Wednesday night, with Shaun Jeffers coming in to make an attacking trio alongside Chris Dickson and Louie Theophanous after Anthony Church and Elliott Buchanan picked up injures. Bagasan Graham also returned to action to sit on the bench.
The hosts began the match applying plenty of early pressure, they created the first chance of the game as full-back Danny Harris burst forward from his position to drive in a cross. The home side attack could not quite take advantage however as Ross Fitzsimons came quick off his line to deal with the delivery.
Dartford continued to create pressure and looked most likely to take the lead from a set-piece, both Elliott Bradbrook and Duane Ofori-Acheampong came close but could not creep their side into a lead.
The Clarets found themselves limited to chances, but they looked most threatening from counter-attacks.
Louie Theophanous’ break down the centre of the pitch saw him edge out to the left channel, before swinging in a cross for striker Shaun Jeffers. However, the City striker could not quite reach the cross as Deren Ibrahim quickly caught the ball.
Dartford almost scored ten minutes before the break when Ryan Hayes’ freekick smacked the post before Chris Bush headed against the post in a goal-line scramble, but eventually the danger was hit away as City remained unscathed.
Max Porter became the first player to receive a booking, on 36 minutes, as he lunged in on Ronnie Vint and caught the defender. Hayes stepped up with the freekick but Bradbrook could not get a head on the delivery.
City came close with a freekick of their own, this time Robbie Willmott saw his curling shot expertly turned over by Ibrahim on 39 minutes to take the two sides into the half-time interval level.
The Clarets came bursting out of the blocks in the second half and immediately applied the pressure. Chris Bush watched as his low drilled shot smacked the post after he expertly worked himself into space, before the defender then almost supplied the assist as Dickson saw his header glimpse the crossbar.
But City eventually went ahead with twenty minutes left. Dickson burst down the left wing before driving a cross for Theophanous, with the striker rising high and powering his header home to send the Chelmsford supporters mental.
The Clarets continued to pressure for a second and it eventually came with five minutes left.
With five minutes left Dickson was sent down the pitch from the half-way line and he unleashed an almighty strike to guarantee the Clarets’ place in the play-off final.
Acheampong almost got the hosts a lifeline in added time, but his driving run came to waste as he poked his shot well over the bar.
But the physical striker eventually grabbed a goal for the hosts but it was too late for the Darts.
The Clarets held on however and deservedly won their place in the final of the Vanarama National League South play-off final.
1. Deren Ibrahim
2. Danny Harris
3. Tom Wynter
4. Tom Bonner
5. Ronnie Vint
6. Alex Brown
7. Ryan Hayes
8. Elliott Bradbrook ©
9. Duane Ofori-Acheampong
10. Andy Pugh
11. Luke Wanadio
12. Lee Noble (55’, on for Alex Brown)
14. Tom Murphy (75’, on for Luke Wanadio)
15. Alfie Pavey (75’, on for Andy Pugh)
16. Keaton Wood
17. Louis Wells
1. Ross Fitzsimons
2. Joshua Hill
3. Luke Daley
4. Max Porter
5. Chris Bush ©
6. Mark Haines
7. Robbie Willmott
8. Josh Rees
9. Louie Theophanous
10. Chris Dickson
11. Shaun Jeffers
12. Ashley Miller
15. Max Cornhill
16. Kane Haysman
17. Lamar Johnson
18. Bagasan Graham (46’, on for Luke Daley)
Chelmsford City: 36’ Max Porter, 61’ Josh Rees.
Chelmsford City: None.
Dartford: Duane Ofori-Acheampong (90+3')
Chelmsford City: Louie Theophanous (70’), Chris Dickson (85')
City Man of the Match: Chris Dickson
Half Time Score: Dartford 0-0 Chelmsford City
Full Time Score: Dartford 1-2 Chelmsford City