Accy's recent run of good form had hoisted them into third place in the league, but that ground to a temporary halt as the Fleet gave the Reds a hard time as they attempted to grab all three points to keep in contention with the leading pack in the Conference.
Ian Craney, scoring his fifth goal of the season gave the home side the start they needed with a drilled shot from 20 yards on 16 minutes.
The visitors however fought their way back into the game and Justin Skinner went close with a free-kick that just went over the bar.
In time added on for injuries at the end of the first half an outswinging corner from the right taken by Kim Grant found Ross Graham-Smith at the far post, but his header went over the bar and with the clock ticking Darren Randolph in the Accrington goal kept out a fine shot from Onome Sodje.
It was Sodje who brought the visitors back into the game midway through the second half.
Liam Daish's Gravesend have been going through something of a transitional period over the past few months, but will have been buoyed by Sodje's 35-yard strike that earned his side a share of the points and moved them into the top half of the table.