The Portuguese kicked out at defender Edimar with seven minutes to go as Real struggled to create chances but they were gifted the win when a Bale free-kick was handled by Fede Cartabia in the area.
Cartabia was also sent off for a second bookable offence and, with Ronaldo off the pitch, Bale fired home the penalty with two minutes left.
Real have been unable to maintain the form that saw them string together 22 consecutive victories in all competitions before Christmas but they remain in top spot in La Liga with 48 points and four clear of Barcelona.
Nabil Ghilas gave Cordoba the lead from the penalty spot with just two minutes played following a handball by Sergio Ramos.
Real lacked rhythm and intensity in their link-up play but Benzema scrambled home an equaliser midway through the first half after Bale flicked on a corner.
Cordoba had looked more likely to win the game and Florin Andone hit the crossbar after 67 minutes with a lob over keeper Iker Casillas.
"I didn’t see what happened and I haven’t spoken with him yet so I can’t make a judgement," Real coach Carlo Ancelotti said of Ronaldo's dismissal.
"You need to win points to be at the top of the table and that is what we have done although it was a difficult game. It was not easy to move the ball around as the pitch was poor."
Second-placed Barcelona, on 44 points, are at lowly Elche later while Atletico Madrid, in third and seven points off the pace, host Rayo Vallecano.
(Editing by Alan Baldwin)
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