Skipper Lee McCulloch opened the scoring with a first half penalty and Ally McCoist's men looked set to hold on for their 21st consecutive win.
But their 100 per cent league record this season was shattered when Jamie Longworth struck for the visitors deep into injury time.
At least there was positive news on the injury front for the Light Blues.
Andy Little made an earlier than expected return to action after initially being ruled out for the rest of the year with a broken cheekbone sustained in early November.
The forward was named on the bench before making his comeback as a substitute early in the second half.
Nicky Law was back in the side after missing the last game against Ayr United through injury, while McCulloch and Lewis Macleod both recovered from a sickness bug to start.
Stranraer found themselves under pressure early on when Nicky Clark attempted to pick out Jon Daly for the header in front of goal but Mark Docherty was able to clear for a corner before the Irishman could connect.
At the other end, Longworth tried his luck with a volley that was well off-target and failed to trouble Cammy Bell.
A powerful run into the box by Lee Wallace culminated in a shot from the left-back that was blocked at the near post by David Mitchell.
The Stranraer goalkeeper was then cautioned for using his hand to deal with a pass back, with Rangers handed a free-kick on the edge of the box.
But they failed to capitalise on the set-piece when the ball was played short to Wallace and his effort fell wide.
Mitchell came to the rescue moments later with a superb save at full-stretch to push Macleod's net-bound shot just over the crossbar.
Rangers were making harder work of this encounter than the last meeting between the sides at Stair Park in August, when all three of their goals were scored within the opening half an hour.
But they were able to breathe a sigh of relief when McCulloch opened the scoring with 37 minutes on the clock.
Frank McKeown was judged to have brought down Clark in the box and the skipper stepped up to convert with confidence from the penalty spot.
With just one goal in the match heading into the break, Stranraer clearly fancied their chances of a comeback in the second half.
And Andrew Stirling was not too far away with an opportune effort from distance that fizzed just past the upright five minutes after the restart.
Rangers made a double switch five minutes later when Arnold Peralta and Clark made way for the introduction of Fraser Aird and Little.
The Northern Irishman could have marked his return to action with a quick goal but he failed to connect properly with a Daly pass and the chance was lost.
Only the woodwork prevented Rangers from doubling their advantage when Law unleashed a well-struck shot that crashed off the underside of the crossbar before the visitors cleared the danger.
A curling free-kick from Stirling was then punched over by Bell, with Stranraer still searching for the leveller.
David Templeton could have ensured the points stayed at Ibrox when he burst past two defenders only to balloon over the bar instead.
Just when Rangers thought they had held on for the win, Longworth lashed home from six yards in injury time to claim a share of the points.