There was one change in the Bluebirds line-up with Darren Purse replacing the injured Gabor Gyepes.
City won a corner in the fourth minute and Purse had a shot hacked off the line as the Rangers defence failed to clear Ross McCormack's flag kick.
Wayne Routledge showed his speed in the tenth minute by out-pacing Mark Kennedy and crossing to Liam Miller but Dimi Konstantopoulos came out smartly to block and the danger was cleared.
Despite jeers every time Routledge touched the ball he was a dangerous outlet for Rangers and one neat backward flick almost saw Heidar Helguson through on goal but Purse snuffed out the danger.
Michael Chopra put Joe Ledley away five minutes before the break but Kaspars Gorkss made a saving tackle and the first half ended with Rangers on the attack.
The Bluebirds were forced into a change during the interval with Miguel Comminges coming on for the injured Kevin McNaughton.
City were now looking more dangerous as Chopra and McCormack at last received some service and both players fired in shots that failed to trouble Rangers keeper Radek Cerny.
Roger Johnson saved City after Damien Delaney was given a free run from the halfway line by pushing the ball behind for a corner just as the Rangers full-back was about to shoot.
In the 65th minute a mis-kick left Chopra free but he skewed well wide with only Cerny to beat.
That was his last act as an ankle injury led to him being replaced by Peter Whittingham a minute later.
Quincy Owusu-Abeyie made his Bluebirds debut in the 73rd minute when he came on for the ineffective Chris Burke.
A mistake by Konstantopoulos, when he cleared the ball straight to Routledge, almost led to the former City loan player opening the scoring but his shot was inches over the crossbar.
Cardiff moved up into fourth place as a result of the point gained but it was a poor home performance against a busy Rangers outfit.