An injury-time strike from substitute Fraser Aird helped Rangers claim their tenth win in a row against Queen’s Park.
The amateur side had looked to have claimed a welcome point despite the sending off of James Brough, but were ultimately denied.
Spiders boss Gardner Speirs made three changes from the side that drew with Elgin City in their last league fixture, with Peter Bradley, Anthony McParland and Aidan Connolly all dropping to the bench to be replaced by Brough, Iain Watt and Lawrence Shankland.
His opposite number Ally McCoist was able to recall Ian Black to the starting line-up along with Robbie Crawford, with Lewis McLeod and Andrew Little both unavailable for the derby fixture.
The game opened up with both sides pushing forward, but neither of them could find the final ball that would bring either Neil Parry or Neil Alexander, guarding their respective goals, into action.
Rangers had the first real chance midway through the half, as Barrie McKay raced down the left wing, before cutting the ball back to the edge of the area, were David Templeton was lurking and the midfielder unleashed a strike just over Parry’s bar.
Some slack passing at the back for Queen’s Park almost saw the visitors take the lead as Lee McCulloch saved the ball from going out of play, then played in Crawford, but the young winger’s strike went wide of goal.
The one-way traffic continued at the start of the second half, with McCulloch receiving the ball just inside the Queen’s Park box, as the Rangers skipper made his way to goal, he attempted to chip Parry, but his effort went just over.
McCoist’s side should have taken the lead when Lee Wallace played the ball into the middle for McKay, he then passed to McCulloch, before receiving the ball back from his skipper and unleashing an effort which Parry had to do well to turn away for a corner.
Things got worse for the amateur side, as Brough received his second yellow card of the game for a challenge on Templeton in the middle of the Queen’s Park half, leaving the Spiders over half an hour with 10 men.
Rangers continued to press forward, with full-back Lee Wallace getting into the box and the former Hearts defender got onto the end of a pass from Templeton, but once again Parry stood up strong in order to deny the league leaders.
The Spiders could have taken a shock lead as Shankland managed to beat his defender on the right wing and swung in a cross for Watt, but his header had no power at all and that allowed Alexander to save easily.
Shankland almost had the visitors worried, as he curled a free kick from the left-hand side, which Alexander was grateful to see go just wide.
Deep into injury time Rangers claimed all three points as Aird picked up the ball on the edge of the area and stroked it beyond the helpless Parry to secure the victory.