The first Cypriot team to ever reach the last eight held out until the 74th minute when Kaka, on as a second-half substitute, crossed for Benzema to score the opening goal.
Kaka tapped in the second in the 82nd after Marcelo went on a determined run to the byline and managed to cut the ball back as he was falling.
Benzema, who missed an open goal in the first half, added his second goal in the last minute of normal time when he connected with a perfect pass from Mesut Oezil.
Madrid coach Jose Mourinho had high praise for APOEL for its performance on Tuesday and throughout the tournament.
"APOEL created many difficulties and I believe we won the game because we played well," Mourinho said. "What they've done, having reached this far is fantastic, and we needed to play to the maximum of our ability to win. They were great in defense and they deserve our respect.
"The dream of the Champions League looks like it's over. It looks very, very, very difficult for APOEL to beat us 4-0 or 4-1 in the Bernabeu. But I think the next dream is to be in the Champions League again."
APOEL coach Ivan Jovanovic agreed that his team's tournament looks certain to end after the return leg on April 4.
"Real has advanced to the next phase of the Champions League, that's for sure," Jovanovic said. "As a team we'll try our best as we have done so far, as we bid farewell to the Champions League.
"I think the score is just. We managed to contain Real as much as we could up to a point. But the pressure on us in the second half was great and, after the first goal, it was easier for Real because there was a sense of disappointment among our players."
But support from the home crowd inside the packed GSP stadium never waned as about 22,000 orange-clad fans chanted ceaselessly, even when their team trailed 3-0. At the start of the match, fans unfurled a giant banner showing a finger knocking down the queen on a chessboard, alluding to Madrid.
Madrid controlled play from the start, besieging the APOEL goal and forcing the Cypriot team into a defensive shell to stifle Madrid's potent attack, which has scored an average of three goals in each of the team's eight previous Champions League matches.
"It was important for us to always be in control, because if you can't win at least you're not going to lose 1-0 and make it difficult for yourself," Mourinho said.
"We knew that the last part of the game would be difficult for them, and we knew that for Kaka and Marcelo to come in when the other team was a bit tired was the right moment to do it."
A volley from an unmarked Oezil from inside the box in the 12th was pushed away by APOEL goalkeeper Dionisios Chiotis.
Cristiano Ronaldo's header from inside the box three minutes later sailed just over the crossbar. In the 28th, Ronaldo latched onto a through pass from Fabio Coentrao inside the box, but his high, angled shot was well saved by Chiotis.
Benzema looked certain to give the visitors the lead their dominance deserved in the 34th when Nuri Sahin delivered a pass across goal — only for the French striker to scoop the ball over the bar from close range and with the goal gaping.
Ronaldo missed again in the 43rd when his flick from Oezil's pass rolled wide.
Nine-time champion Madrid continued to be frustrated in the second half.
Ronaldo misses with a long-range effort in the 49th before his free kick in the 67th cannoned off the wall and fell for Oezil, whose shot was blocked.
APOEL, meanwhile, were limited to a few attacking forays by Brazilian forward Ailton Almeida.
Madrid finished the match with 20 attempts on goal to APOEL's zero, but it took the introduction of Kaka in the 64th minute to provide the spark for the visitors to emphasize the gulf in class.