Luke Garrard gave Wood a first-half lead with a penalty but missed a second spot-kick. Lee Miller headed Carlisle level in the closing stages and Mark Beck pounced for the winner four minutes into injury time.
The Conference South side, 72 places below Carlisle in the football pyramid, showed no signs of being overawed and might well have grabbed an 11th minute lead when Greg Morgan cut in from the right and slid a shot just inches wide with keeper Greg Fleming struggling to get anywhere near the ball.
Wood did get their reward for a solid start when Arsenal youngster Austin Lipman, on loan to the non-league side, got the better of Pascal Chimbonda and was brought down inside the box. Garrard gave Fleming no chance as he hammered the penalty into the top right hand corner.
The visitors should have gone two up a couple of minutes later when Conor Townsend's challenge on David Moli resulted in a second penalty, but this time Fleming guessed correctly, diving to his left to save Garrard's effort.
When out-of-sorts Carlisle finally got a shot on target after half-time, Wood skipper Charlie O'Loughlin came to the rescue, hacking Liam Noble's drilled low right footer off the line.
All the second-half pressure came from Carlisle and it eventually paid off 10 minutes from time when Miller got his head to David Symington's cross from the left and looped the ball past James Russell from six yards out.
Boreham Wood's brave resistance was broken in the fourth minute of added time when Russell was unable to hold on to James Berrett's stinging low drive and substitute Beck pounced to slot the loose ball home.