Real overcome gritty Rayo
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 this evening after a suspected act of sabotage saw the power supply cut at the Estadio de Vallecas yesterday.
Tonight's victory was just Real's second win in five La Liga matches and the defending champions are now eight points behind frontrunners Barcelona. "We played as a team but we could still have been better. We were committed, which is important and it allowed us to win without problems," said Mourinho afterwards.
"It has been a strange situation with the postponement and it has been complicated to prepare for this but it was the same for both teams. We overcame it and although it wasn't a great win, we did enough. We had a lot of chances to score while they had few."
Real weathered an early barrage and could have been ahead in their first real attack, but Pepe's free header at the back post forced an acrobatic save from Vallecano goalkeeper Martinez Ruben.
The warning signs were there for Paco Jemez's side, but they could do nothing as Real countered to great effect in the 13th minute. Ronaldo released Angel Di Maria down the left and he was inexplicably allowed to cut into the area and pick out Benzema, who tapped into an empty net at the back post.
Vallecano had not learned their lesson and only Di Maria's selfishness - the winger's shot curled wide from 25 yards when better options were ahead of him - prevented Madrid from doubling their lead, once again on the break.
Ronaldo forced Ruben to make a fine save at his near post while the Vallecano stopper rushed out to save point blank from Luka Modric, who had latched on to Di Maria's chip into the box. Real's failure to extend their lead then nearly came back to haunt them as first Iker Casillas reacted well to parry away Jordi Amat's bullet header before Mikel Labaka's follow-up effort was chested off the line by a covering Xabi Alonso.
The visitors did end the half in convincing fashion, though, with Di Maria and Benzema linking up once again, ending in the latter's strike across goal being tipped away by Ruben.
Vallecano started the second half in a positive fashion, although Andrija Delibasic was caught unawares when Real defender Alvaro Arbeloa's woeful back-pass picked out the Montenegro striker on the six-yard line.
And he was nearly made to rue his lapse in concentration a few minutes later when Benzema sprinted clear and slotted past Ruben, but the referee had already blown his whistle for a Madrid free-kick in the build-up.
It was only temporary respite for a game Vallecano outfit, who fell further behind in the 70th minute when Ronaldo's cut-back was handled by a sliding Jordi Amat, with referee David Fernandez Borbalan awarding the spot-kick. The former Manchester United man fired home, sending Ruben the wrong way.
Ronaldo should have made the game safe moments later but he embarrassingly chipped onto the bar - under pressure from Triguero Tito - from close range with the net gaping after a selfless assist from the recently-introduced Gonzalo Higuain.
It mattered little, however, as Jose Mourinho's side comfortably saw out the remaining few minutes for their first victory on their travels this season.