Doubles from Scott Arfield and Graham Barrett were enough to see off the first division side, who led briefly in the second half.
The horrendous conditions made life difficult for both sets of players with Queens facing a strong wind in the first half.
Falkirk fashioned an early chance when a deep cross from Jackie McNamara picked out Barrett at the far post and his close-range header was tipped over by Lee Robinson.
Craig Barr was in the right position to block a header from Barrett in front of goal after a great cross from Neil McCann.
Too often, Falkirk managed to get to the edge of the penalty are but then chose the wrong option, much to the frustration of their fans.
But Falkirk got the break they needed eight minutes from half-time when referee Charlie Richmond ruled that Barr had fouled Barrett in the area.
Arfield expertly sent Robinson the wrong way with the spot-kick to put the Premier League side ahead.
But Queens were level four minutes later when Falkirk failed to clear their lines and Barry Wilson scored with a deflected 16-yard shot.
The first division side took the lead two minutes after the break when Steve Tosh touched a short free-kick to Robert Harris and he thundered in a wind-assisted left-foot shot.
But Falkirk equalised within a minute when McCann's cross was missed by Barr and Arfield netted with a low shot.
A mistake by Barr on the edge of his own area gave Stewart Kean a chance to put Queens ahead again but he lacked composure and sent his shot high and wide.
Michael Higdon was just inches away at the other end after he managed to get his head to a Lee Bullen cross at the far post but could not direct his effort on target.
Queens did not heed the warning and it was 3-2 after 68 minutes when Robinson reacted well to stop a Barr shot with his right hand but Barrett was alert to slam the loose ball into the net.
The Irish striker completed the scoring ten minutes from time when he shot home after great work down the left by Mark Stewart.