It was a solid and professional performance from the Tudors, who took the lead after 33 minutes.
Spencer McCall’s header dropped on the edge of the area for skipper Jordan Parkes to acrobatically finish past Lucas Lidakevicius into the bottom corner.
And 9 minutes later, Hemel doubled their advantage when more good work from McCall saw his cross is missed by a defender, leaving Sanchez Watt to pick up the loose ball and tuck the ball into the net at the near post.
The Tudors almost made it 3-0 shortly before the break when David Moyo got on the end of a Kyle Connolly header 10 yards out, but it bounces off the post.
The second half was all about game management for the home side and East Thurrock were mainly kept at arms` length.
But there was a rather bizarre incident 10 minutes from time when the referee pulled out a red card to Sanchez Watt, presumably for dissent.
However, the colour of the card changed to yellow.