Both sides started in the top seven and both were looking to put pressure on leaders Dartford.
Jordan Parkes opened the scoring in the 25th minute from the penalty spot after Mark Haines was penalised for a foul on Will Hoskins.
And in the 35th minutes Parkes put the Tudors in command with his second directly from a left-wing corner as debut `keeper Nathan Gartside was caught out of position at the far-post.
Chelmsford boss Rod Stringer was dismissed from the dug-out midway through the half after disputing the legality of the second goal.
Then in the 84th minute, the Tudors put the result beyond the Clarets with a fine curling effort from Spencer McCall.
Chelmsford sub Thomas Hitchcock was given a straight red card late in the 86th minute for an alleged elbow incident.
And Scott Davies grabbed a stoppage time consolation goal for City, but it was too little too late as Hemel slipped into third place, three points behind the Darts, while the Clarets remain in seventh spot.