Benzema finished a fine counter-attack to give Real a deserved 13th-minute lead and they survived a few nervy moments before Ronaldo made the game safe from the spot midway through the second half in an encounter held over until Monday evening after a suspected act of sabotage saw the power supply cut at the Estadio de Vallecas 24 hours earlier.
The victory was just Real's second win in five La Liga matches and the defending champions are now eight points behind frontrunners Barcelona.
Real coach Jose Mourinho said “If we had played other Liga matches with a similar attitude we would have won them. It was a difficult match that required absolute concentration and motivation. I believe the team has responded well."