Sean O'Hanlon hit the post for Carlisle in the first half, but the Skrill South side were always in the contest and almost scored themselves through Graeme Montgomery's fine strike before settling for a replay.
A scrappy opening came to life after 12 minutes when striker David Moli, on loan at Boreham Wood from Wolves, turned sharply and forced Mark Gillespie into a save.
O'Hanlon almost gave Carlisle the lead when his header came back of the post before being cleared off the goal-line by Callum Reynolds.
Wood goalkeeper James Russell superbly tipped over Lewis Guy's 10-yard effort, but the hosts almost took the lead through Montgomery's dipping long-range volley that Gillespie tipped over three minutes before half-time.
Moli fired narrowly wide from a short corner at the start of the second half and then Austin Lipman, on loan from Arsenal, saw a 20-yard strike clear Gillespie's crossbar.
It took until the 76th minute for Carlisle to force Russell into another meaningful save, the keeper this time turning behind second-half substitute David Symington's low drive before James Berrett drove into the side netting near the end.