The exciting Argentinian, who scored a Carling Cup hat-trick in the week, collected his cards within five minutes either side of the break.
The first, for a tackle on City's persistent Brian Wilson, was harsh, the second, which put his victim, Jamie McAllister, out of the game, was very late, catching him on the shin after the player had crossed the ball.
It was a tackle which didn't matter, as the linesman was already signalling the ball had gone out of play.
Ledesma, with his touch, and bending ball had been the driving power behind Rangers' attacks and without him to inspire them, they were left looking for ways to escape with a point.
This largely consisted of pulling everyone except Dexter Blackstock back into the box each time City threatened.
Even so, they so nearly snatched the winner when Blackstock broke away after Scottish centre-back Andy Webster, who had come on for McAllister, had been woefully slow into a challenge.
City, sensing a win, attacked in waves but without imagination. They failed to use the wings to stretch Rangers' defence and when they got through found Radek Cerny in goal at the top of his game.
One of his late saves, a dive to the foot of his post to squeeze away a ten-yard header from Dele Adebola, should be comfortably up there in the ten best saves of the season.
Adebola had scored City's equaliser with a sharp move at the end of a typical surge in the first half to meet Wilson's low ball in from the left.
Rangers had gone ahead six minutes earlier through Blackstock, who shook off a challenge from Louis Carey and a tackle from goalkeeper Adriano Basso to prod his shot into the far corner.