The Conference rivals had to settle for a replay after a scrappy qualifying round clash at St James's Park.
There were chances at both ends but it was an afternoon when defenders were always on top.
The visitors started brightly. Tiny striker Ben Abbey thumped a long-range shot over the bar and Rob Haworth caused problems with a fine run into the box in the opening minutes.
Exeter were strangely lethargic throughout much of the opening period. Justin Skinner struck a shot past the post from 30 yards as the Kent part-timers did most of the early work.
Exeter's best early moment came when Steve Flack picked up a loose ball a thumped a fine shot just over the bar from 25 yards.
Barry McConnell launched a fine run on the right but was unable to pick out Flack in a rare Exeter attack.
Scott Hiley picked out Flack with a fine cross from the right but the striker was unable to direct his header towards goal.
Exeter enjoyed their best spell just before half time. Hiley linked well with McConnell and the winger's cross was headed just past the post, and Dwane Lee fired a shot into the arms of the goalkeeper.
After the break Sean Canham headed into the arms of the goalkeeper from Alex Jeannin's corner then struck weakly shot at the goalkeeper after he was found by Glenn Cronin.
Gravesend always posed a threat. Abbey burst into the box and found Haworth who struck past the post. Abbey then had a shot deflected wide before Steve McKimm shot into the arms of the goalkeeper.
McKimm found Ben Walshe in plenty of space but his shot was well saved by Martin Rice as the visitors sensed victory.
The closest Exeter came was when Flack glanced a header against the bar from Gareth Sheldon's corner in the closing stages.