Leading 2-0 from the first leg, Real peppered the visitors’ goal, although Edin Dzeko and Mohamed Salah wasted chances for Roma at the Bernabeu.
It proved costly as Ronaldo crashed in at the near post before setting up James Rodriguez for an angled finish.
Roma hit the post but Real made the last eight for a sixth successive term.
With Zinedine Zidane’s team 12 points behind La Liga leaders Barcelona, and disqualified from the Copa Del Rey, winning the Champions League remains their only realistic chance of silverware.
And although the 10-times winners impressed in attack, their casual approach to defence, particularly from left-back Marcelo, will give more potent teams hope.
Roma will now return to Serie A, where they lie third, after winning their last seven successive league games.
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