Clarets captain Alexander, who uncharacteristically missed his last penalty back in September, stepped up in first-half stoppage time to hit the first league goal Rangers have conceded at Loftus Road this season.
The spot-kick, awarded after Matt Connolly felled Dean Marney, cancelled out a stunning strike from Adel Taarabt and meant Cardiff leapfrogged Neil Warnock's side at the summit.
It may be harsh to suggest Rangers' form is stuttering after they extended their club-record unbeaten start to the season to 14 games.
But four successive draws suggest the division will not be the cakewalk it appeared a month ago when the Hoops were steamrollering everyone in sight.
Paddy Kenny had not picked the ball out of the home net for more than nine-and-a-half hours, but he had to make a double save early in the first half to extend his record by a few minutes.
Kenny probably should have held Chris Eagles' 20-yard drive but when he spilled the ball at the feet of Jay Rodriguez, the big keeper recovered superbly to palm his effort clear.
Burnley felt they should have had a penalty on the half-hour when Eagles tumbled under Clint Hill's challenge but referee Iain Williamson booked the Clarets winger, despite having earlier ignored a risible dive by Taarabt.
But if that was the worst side of Taarabt's game, the mercurial Moroccan soon showed the best by lashing an unstoppable 25-yard curler past Lee Grant and into the top corner in the 33rd minute.
Rangers could have been two up three minutes later but Rob Hulse and Alejandro Faurlin merely got in each other's way as they went for Taarabt's cross.
Instead, they allowed Burnley to draw level on the stroke of half-time when Kenny's goal was finally breached.
Connolly clumsily bundled Marney over in the area, Williamson this time pointed to the spot and Alexander duly obliged.
Rangers came closest to a winner in stoppage time when Tommy Smith curled inches wide and Shaun Derry crashed a shot over.
Burnley had their chances too, with Chris Iwelumo lashing his shot high over the bar and Rodriguez's toe-poke bouncing narrowly wide of Kenny's goal.
But even Rangers co-owner Bernie Ecclestone, on a rare Grand Prix-free weekend, had seen enough before the end as both sides settled for a point.