The draw was enough for Queens as relegation rivals Stanraer lost to St Mirren and they will go into a play-off.
Queens attacked from the start and went close in two minutes when Paul Burns forced a save from goalkeeper Craig Nelson.
Brechin hit back and David Hannah laid the ball off for Stuart Callaghan to shoot wide then a Hannah drive from 30 yards was saved by Ritchie Barnard.
Back came Queens and in 20 minutes Sean O'Connor shot just wide from a Graham Weir pass.
Queens scored a vital goal in 22 minutes when O'Connor rose high to power home a header from a Ryan McStay free-kick.
Brechin hit back immediately and Graham Gibson was unlucky to head wide and then in 29 minutes Hannah headed over from a Callaghan free-kick.
In 40 minutes Queens went close again when John O'Neill drove over from a good position. Two minutes later a run from Burns ended with the ball going to O'Neill and his shot was saved by Nelson.
In 57 minutes O'Neill headed wide from a McStay corner but Brechin refused to give up and in 68 minutes Chris Geddes headed wide from a Callaghan corner.
Brechin were out of luck in 76 minutes when a Chris Templeman header from a Callaghan free-kick was cleared off the line by Stuart Lovell.
Brechin got a deserved equaliser in 79 minutes when Barnard was penalised for carrying the ball outside his box and Callaghan stepped up to drive home the free-kick.
Brechin battled to the end and in 89 minutes Geddes drove into the side-netting after a neat move then in stoppage time Geddes shot over from a good position.