The Clarets conceded within minutes of kick off before Rhys Murphy's tap in levelled the game. It looked like it would be a stalemate heading into half time until the referee controversially ruled out his assistant's offside flag to award Dulwich a penalty.
Chelmsford equalised with a penalty of their own early in the second half, but neither could find a winning goal despite several good chances.
After ping pong in Chelmsford's defensive third in the fourth minute, the ball fell to Nyren Clunis on the outside of the box, who duly slotted into the net down to Ross Worner's right hand side.
It was almost a second goal for Dulwich Hamlet after a calamitous error from Jazzi Barnum-Bobb just before the 20 minute mark. The right-back intended to pass back to goalkeeper Worner, but fluffed his kick, putting Anthony Cook through on goal. Worner pulled off a smart save on the shot destined for the far corner and danger was averted.
Murphy was the width of the post away from equalising in the 24th minute. Omozusi's freekick from the centre circle fell to the striker mere feet from Dulwich's left hand post but his audacious overhead kick rippled against the side netting.
It was Murphy who atoned for the miss with the equaliser a minute later though, when Scott Fenwick squared across the penalty area for an easy tap in inside the six yard box.
Murphy nearly had a brace within six minutes. Barnum-Bobb made a lung-bursting run down the right hand flank, leaving Dulwich's left-back for dead, crossed into the middle of the box and the number 19's volley sailed just wide.
Chelmsford were right on top on Dulwich towards the end of the first half, winning a succession of corners and forcing Preston Edwards in some key saves: the most impressive being a tip over his crossbar as he was falling backwards.
Jay May had a golden chance to get Dulwich back into the lead in the minutes before half time. Clunis' cross found him deep inside the Clarets' penalty area but the striker couldn't sort his feet out and missed the ball when he really should have scored.
Chelmsford's sloppiness at the back could have cost them again in the 45th minute. Clunis got in behind and his lashed shot from a tight angle was saved by Worner at the near post.
Controversy reigned in the seconds before the break as Dulwich were awarded a penalty - but it seemed to have been ruled out by the linesman's flag. After a long discussion between referee and linesman, the spot kick was given. Carew stepped up and put his shot into the top corner, in spite of Worner getting a glove on it.
The sides went in at half time with a chorus of boos from the home fans towards the officials. Upon reviewing the recorded footage, there was clearly an offside Dulwich player before the foul that led to the penalty.
The officials reappeared for the second half to another throng of booing, before the home faithful refocused to cheer on their players.
The incident definitely hadn't been forgotten about though: Dulwich's first offside of the second half was met with a round of rapturous ironic cheering and applause from the City fans.
City were given retribution 10 minutes into the second half when they were awarded a spot kick of their own: Fenwick calmly slotted it powerfully into the bottom left corner.
Tom Wraight went very close to putting Chelmsford ahead for the first time in the game in the 65th minute. The ball was passed across the box to Wraight who was in acres of space but the midfielder's shot was too high.
Dulwich may have been under the cosh, but Chelmsford weren't looking too tight at the back themselves, and were it not for Cook completely missing a side foot shot inside the area, and Clunis being denied by a sprawling defender at the far post, City would've been several goals worse off.
Fenwick went mighty close to making it 3-2 in the 71st minute. The number nine cut in from the left of the box and drove a shot at the near post but he could only find the side netting.
Following the trend of shooting over was Anthony Church, who found Edwards' parry fall to him outside the area but couldn't control the shot.
Somehow, Chelmsford didn't score in the 78th minute. Shaun Batt's quick throw found Murphy who lost his marker and passed to Church, whose shot was remarkably saved by Edwards and trickled just wide past the post.
Clunis should have got Dulwich's third with seven minutes of normal time remaining. Afolabi Dipo Akinyemi got past Joe Anderson down the left and crossed for Clunis who's low shot was met at close quarters by Worner.
Lawrence's speculative shot from 20 yards was the last action of the game. A hard fought draw was a fair result considering the controversial penalty and plethora of missed chances by both sides.
1. Ross Worner
2. Jazzi Barnum-Bobb
3. Elliot Omozusi
5. Michael Spillane
8. Anthony Church (captain)
9. Scott Fenwick
11. Tom Wraight
13. Joe Anderson
16. Amos Nasha –
18 Chris Whelpdale
19. Rhys Murphy
10. Jai Reason (53’, on for Amos Nasha)
12. Taylor Miles
14. Mark Haines
15. Matthew Foy (85', on for Chris Whelpdale)
17. Shaun Batt (75’, on for Scott Fenwick)
Dulwich Hamlet :
1. Preston Edwards
2. Quade Taylor
3. Sanchez Ming
4. Ibrahim Kargbo
5. Magnus Okounghae (captain)
6. Daniel Pappoe
7. Nyren Clunis
8. Ashley Carew
9. Jay May
10. Dominic Vose
11. Anthony Cook
12. Byron Lawrence (75’, on for Anthony Cook)
14. Afolabi Dipo Akinyemi (59’, on for Jay May)
15. Nathan Ferguson (72’, on for Ashley Carew)
16. Gavin Tomlin
17. Walter Figueira
Chelmsford City: Rhys Murphy (25'), Scott Fenwick (58' Pen)
Dulwich Hamlet: Nyren Clunis (4'), Ashley Carew (45+5' Pen)
Chelmsford City: Michael Spillane (45+5'), Tom Wraight (79').
Dulwich Hamlet: Ibrahim Kargbo (76'), Daniel Pappoe (90+2'), Sanchez Ming (90+2').
Chelmsford City: None
Dulwich Hamlet: None.
Half time: Chelmsford City 1 - 2 Dulwich Hamlet
Full time: Chelmsford City 2-2 Dulwich Hamlet