The hosts went ahead through Jai Quitongo in the first half, and looked like they would see out the three points until a late flurry from Kenny Miller’s side saw them nearly pick up all three points.
In the end a win would have meant nothing, with the Bairns just happy to end what has been one of the worst seasons in the club’s history.
The first chance of the match fell to the home side with Celtic loanee Luca Connell testing Robbie Mutch with a deflected effort from just outside the box that was safely collected.
Ex-Bairn Bob McHugh was next to have an effort, blasting an overhead kick well over the bar.
Falkirk hadn’t created any clear cut chances but looked much more creative in attacking areas with Leigh Griffiths being supported by Anton Dowds and Callumn Morrison.
The Bairns first real chance came from Dowds’ shooting from distance.
His shot swerved at the last moment to go past Callum Ferrie’s near post.
Queen’s Park opened the scoring on the half hour mark after a Falkirk corner came to nothing.
Connell burst forward and caught out a sleeping Bairns defence before feeding in Jai Quitongo, who slotted home past Mutch.
He then went close with an effort five minutes later as the Bairns struggled to hold onto possession.
The goalscorer Quitongo thought he had found the back of the net again on 42 minutes when he headed home at the back post, but he was adjudged to have fouled Leon McCann in the process.
Despite the pressure from the Firhill hosts, Griffiths nearly levelled the match before the half time whistle with a low-driven free kick that was well saved by Ferrie.
The Bairns started the second half well and Telfer was denied an equaliser by McHugh, with the striker clearing off the line from the midfielder’s effort.
Griffiths then should have done better with a free header in front of goal after a perfect cross from Morrison found him.
The Spiders had their first effort through McHugh, who shot through a sea of bodies and nearly caught Mutch out.
A flurry of substitutions left the tie feeling like a training match and chances were at a premium.
However, Morrison caught the ball on the edge of the box sweetly and fired home a wonderful strike to level the match on 83 minutes.
The Bairns then looked for a winner and Telfer and Nesbitt both had shots blocked as the hosts camped around their own box.
However, Owen Coyle’s side held out for a point.