If they can stay unbeaten to the end of the season, it would equal the 1974 club record of 20 games without defeat.
"We've got five to go and we want to go five unbeaten. That'll be 20 games unbeaten which is a fantastic record," Hessenthaler told BBC Radio Kent.
"We've got that bit between our teeth and we can achieve that.
"We've still got to go to Rotherham, and to Chesterfield in the last game, but there's no reason why we can't make that record - I'm sure we will."
Saturday's win leaves the Gills, who were languishing in the bottom three back in November, in seventh, one of three teams on 64 points.
And they still have hopes of an automatic place, just four points adrift of third-placed Bury.
"We've got nothing to lose - let's just go for it," said Hessenthaler. "That's what I've told the players - relax and just go for it.
"They've worked so hard to get us in this position so don't go and throw it all away now because this season will fizzle out.
"There's no pressure, just go and enjoy it."
Source: BBC Sport
Source: BBC Sport