The visitors raced into a three-goal lead thanks to a goal from Ross Draper and a double from Colin Daniel.
Danny Jackman's strike gave the Gills hope but Emile Sinclair scored early in the second half to ensure Joe Martin's strike was only a consolation.
The defeat ensured the Gills missed the chance to move back into the play-off places.
An angry Hessenthaler said: "This is the second game in a row where we've defended like schoolboys. The problem is we're so Jekyll and Hyde at the moment.
"We didn't give ourselves a chance - you can't concede three goals in quick succession like that - you give yourself a mountain to climb. We're not out of it (the play-off race) - people may think we're out of it - maybe our own people think we're out of it but we've got a shot."
Source: PA
Source: PA