Ryan Bird opened the scoring early in the first half but it was all square at the break with Conor Wilkinson, having missed a penalty, finishing well from close range.
The visitors took the lead through Luke O'Neill but Giancarlo Gallifuoco took advantage of a Tomas Holy error to ensure the shares were spoiled.
Boss Ady Pennock was true to his word with the team who finished the game at Dartford getting the nod to start at Crabble.
Gills started well but found themselves behind within seven minutes.
Femi Ilesamni produced a fantastic cross towards Ryan Bird and the striker made no mistake in diverting his header beyond Stuart Nelson into the bottom right hand corner.
The Whites continued to press with Kane Richards nearly connecting to Mitch Brundle's cross, with Hessenthaler at the other end sending an effort off target following a great run by Connor Ogilvie.
Gillingham were presented with a golden chance to equalise on 27 minutes when Trialist was fouled inside the box by Giancarlo Gallifuoco.
Wilkinson stepped up but Mitch Walker read it brilliantly and got down low to his left to palm away the effort.
However the striker soon made up for it, a few minutes later Trialist did well to provide a low pass into the box. The ball took a slight deflection but Wilkinson got on the end of it and drilled an effort beyond Walker.
Gills finished the half strongly with Ogilvie nearly creating an opening before former defender Connor Essam brought his run to a premature halt.
Gills didn't take long to register their first attack. O'Neill latched onto a Martin corner but his header was comfortably dealt with by Walker.
Martin decided to go it alone shortly after; Ogilvie played a short pass and space seemed to open up for the midfielder. With no other options he had a go for goal but his effort was wide of the left hand upright.
However on the hour mark Gills did finally take the lead. One of the visiting trialists whipped in a great ball from a free-kick and O'Neill got in front of his marker to power a header beyond the helpless Mitch Walker.
The new look XI took to the field immediately and within a minute it was all square again. A flick on from a set piece should have been dealt with by Tomas Holy but the ball seemed to slip through his hands and Giancarlo Gallifuoco had the simple task of converting from close range.
The keeper made up for his error by showing bravery to block the ball with his head, and although he was beaten again, this time by Tobi Sho Silva, the bar came to his rescue when the effort cannoned back off the woodwork.
With the clock ticking down the best chance to force a winner fell to the visitors. Sub Darren Oldaker pinged a ball to a trialist at the back post who sent his volley over from inside the box.
Dover Starting XI: Walker, Trialist, Ilesamni, Gallifuoco, Parry, Essam, Richards, Brundle(c), Bird, Allen, Trialist.
Gills team (First 60 mins): Nelson, O'Neill, Zakuani, Trialist, List, Hess, Byrne, Martin, Ogilvie, Trialist, Wilkinson.
Gills team (last 30): Holy, Ehmer, Tucker, O'Mara, Garmston, Trialist, Oldaker, Wright, Wagstaff, Stevenson, Mbo.
Gills subs: Hadler, Simpson, Chapman, Cundle.
Referee: Mr G Maskell