Match ends, Queen's Park 1, Rangers 2.
Kris Boyd headed a double to edge Rangers past a spirited Queen's Park in the League Cup.
Boyd nodded in after seven minutes but a mistake from keeper Steve Simonsen allowed Tony Quinn to level.
The prolific striker then came to the visitors' rescue from close range shortly after the interval.
Simonsen redeemed himself with a point-blank save from Ross McPherson's header before Lewis Macleod hit the post for Rangers, who play Inverness CT next.
There was no sign of the struggle to come for Ally McCoist's side in the opening stages of the first-round tie, which had been delayed by the Commonwealth Games, and only a wonderful save from William Muir prevented Lee McCulloch heading home Nicky Clark's cross.
The opener came when Boyd headed into the roof of the net from six yards following a pinpoint right-wing cross from Nicky Law.
Boyd had a shot saved from 20 yards as Rangers probed for a second but they had lost their early edge and the amateurs got a foot hold in the game without threatening.
But the Spiders were gifted an equaliser in the 31st minute when Simonsen came way off his line in an attempt to catch Darren Miller's free-kick from just inside the Rangers half.
The 35-year-old, deputising for the injured Cammy Bell, did not get there and Quinn steered the ball into the empty net.
Bilel Mohsni came close with a diving header before the visitors regained the lead in the 53rd minute.
The home defence were stretched as Rangers piled men into the box and Arnold Peralta latched on to McCulloch's blocked shot and lifted the ball into the six-yard box for Boyd to nod home.
A great block from David McGregor prevented Clark from adding to the lead following a strong run from Lee Wallace.
Simonsen then kept out McPherson's header before Macleod hit the frame of the goal from 22 yards and then arrowed a shot just over the top.
- 7WoodsBooked at 15minsSubstituted forMcElroyat 83'minutes
- 4BerrySubstituted forCarterat 88'minutes
- 10FraserBooked at 47mins
- 11FotheringhamSubstituted forBurnsat 27'minutes
- 24McGregorBooked at 90mins
- 7LawBooked at 44minsSubstituted forBlackat 76'minutesBooked at 82mins
- Alan Muir
- Shots on Target
Second Half ends, Queen's Park 1, Rangers 2.
Foul by Ross Gallacher (Queen's Park).
Nicky Clark (Rangers) wins a free kick in the defensive half.
Attempt missed. Ross McPherson (Queen's Park) right footed shot from outside the box is too high from a direct free kick.
Darren McGregor (Rangers) is shown the yellow card.
Ciaran McElroy (Queen's Park) wins a free kick in the defensive half.
Foul by Darren McGregor (Rangers).
Substitution, Queen's Park. John Carter replaces Vincent Berry.
Ciaran McElroy (Queen's Park) wins a free kick on the left wing.
Foul by Arnold Peralta (Rangers).
Substitution, Queen's Park. Ciaran McElroy replaces Paul Woods.
Ian Black (Rangers) is shown the yellow card.
Vincent Berry (Queen's Park) wins a free kick in the defensive half.
Foul by Ian Black (Rangers).
Attempt missed. Nicky Clark (Rangers) header from the right side of the six yard box is close, but misses to the right.
Corner, Rangers. Conceded by Tony Quinn.
Substitution, Rangers. Ian Black replaces Nicky Law.
Corner, Rangers. Conceded by Gavin Mitchell.
Attempt missed. Lewis MacLeod (Rangers) right footed shot from outside the box is too high.