Dover were in big trouble when their former player-boss returned to take charge back in October.
But he has been able to drag the club from the bottom four and they now have an eight-point advantage over the teams in relegation zone.
They would have been as good as safe had they held on for victory at Solihull Moors on Saturday.
Having twice lead, the title chasers netted a late leveller as Dover returned home with only a point from the 2-2 draw.
But Hessenthaler knows if they continue to play how they are then they will avoid the drop into the National League South.
“It’s difficult as we were so close to three points,” the manager said.
“It’s happened a few times this season now, nobody likes dropping points in time added on.
“But I thought the players were great and we nearly made it three wins in a row.
“We’re fighting and that’s what you need at this stage of the season when you are where we are in the table.
“If we carry on doing that we’ve got every chance of achieving what we set out to do.”
Next up for the Whites is a home game with Chesterfield.