The home side enjoyed the bulk of possession in the early stages but clear-cut chances were few and far between.
The breakthrough came in the 35th minute, however, when Steven Rennie put Arbroath ahead, heading a Jay Stein corner powerfully beyond Kieron Renton.
Elgin hit back immediately, Martin Johnson taking advantage of the lack of concentration in home defence to slot the ball low past Mark Peat for the equaliser.
The visitors almost snatched a lead in the 41st minute when David Hind's 20-yard shot was tipped over the bar by Peat.
Arbroath started the second half brightly with Alan Brazil hooking a shot narrowly over.
Then Rennie came close with a header which Renton pushed behind.
Elgin clawed their way back into the game and Adam Moffat had a great chance to put them in front when he invaded the Arbroath defence, but his shot hit Peat's left-hand post and the danger was cleared.
A few minutes later Arbroath took what proved to be a winning lead when Brazil latched on to a through ball from Paul Watson, shrugged off a Hugh Dickson challenge and slotted the ball beyond Renton.
The home side continued to dominate with Willie Martin and sub Nicky Smith both coming close in the latter stages of the game.