Ollie Pearce’s opener was cancelled out by a first half brace from Ambers’ Roman Liburd.
Cheshunt started the game on the front foot, with former Worthing man Zack Newton crossing the ball into Rowan Liburd, who tried to catch Harrrison Male at his near post but got down to make the save.
However, Worthing responded well and in the 10th minute Reece Meekums broke into the Cheshunt penalty area, and found Ollie Peace who squeezed the ball into the far corner to put the hosts 1-0 up.
Cheshunt continued to cause Worthing problems on the break and after a probable foul on Meekums by Joe Re, the midfielder slipped in Rowan Liburd who fired past Male to put the visitors level.
On the half hour mark, a mix up at the back for Worthing saw Jesse Starkey dispossessed inside the Worthing penalty area, with the ball falling to Liburd who smashed home to put Cheshunt 2-1 ahead at the interval.
Worthing came out for the second half on the front foot, and almost found an equaliser on the hour mark, with Starkey whipping in a corner deep to Racine at the back post, but his header was put wide.
10 minutes later, Pearce was slipped in after a lovely one-two with Cox, and sold a dummy to Chevron McLean to put him through on goal, but Marsh was equal to his effort.
Worthing continued to press for an equaliser in the final ten minutes, with Racine coming close in the 84th minute with a header from a Marvin Armstrong cross which looped over the bar and onto the roof of the net.
Controversy struck the match in injury time when Starkey crossed the ball into Dean Cox.
He powered his header into the arm of a Cheshunt defender, however the referee waved the Worthing penalty appeals away and awarded a corner.
In the final minute of added-on time, Cox footed a lovely-disguised pass into Golding lurking inside the six yard box, but the striker volleyed his effort onto the crossbar.
Worthing are five points clear in top spot and host Seaford in the Sussex Senior Cup on Tuesday.