Rovers went into tonight's second leg at The New Lawn with a 1-0 lead after the first leg, and Keanu Marsh-Brown scored what proved to be the decisive goal to earn his side a 1-1 draw on the night.
Ricky Miller was the next to threaten for the visitors, but he couldn't keep his shot down after creating space to shoot from outside the Forest Green penalty area.
Dover were soon back on the offensive, however, with Stefan Payne turning well inside the Forest Green penalty area only to fire his subsequent effort off target.
Brett Williams came close to breaking the deadlock midway through the first half when he danced his way into space before seeing his shot saved by Walker.
The visitors should have opened the scoring with 10 minutes of the first half remaining when Miller was presented with a gilt-edged chance from just a few yards out, but he failed to hit the target.
Forest Green ended the half on top, though, and had two efforts before the interval as both Marsh-Brown and Charlie Clough fired shots over the crossbar.
It was Dover who came out quickest for the second half, though, and it took a smart save from Arnold to deny Ricky Modeste just two minutes after the restart.
The visitors were ahead shortly after, however, when Miller's shot deflected off Ben Jefford to leave a wrong-footed Arnold helpless.
That levelled things on aggregate, but Dover enjoyed parity for just five minutes before Marsh-Brown put his side back ahead in the tie.
Dover were inches away from taking the lead once again shortly after the hour mark when Sam Magri fired a powerful effort on goal, only to see it hit the underside of the crossbar before being cleared.
Marsh-Brown almost curled in a second of the night to put the tie to bed in the closing stages, but Forest Green did hold out to book a trip to Wembley, where they will face either Grimsby Town or Braintree Town.