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.

Ronaldo settles Bernabeu nerves

Strangely for a game where Real wracked up 37 shots, Roma had the better opportunities and could have changed the mood inside the Bernabeu if Salah and Dzeko were more clinical.

Ronaldo did miss a great chance to double his lead, but having been out of favour with Real fans after his seemingly critical comments about team-mates following the 1-0 defeat by Atletico Madrid on 27 February, he proved his value once again.

Early on, Real's leading scorer appeared to be trying too hard to win supporters over, occasionally guilty of showboating rather than taking the chance to shoot.

Once he stung the hands of Roma goalkeeper Wojciech Szczesny either side of half-time, he finally opened the scoring when he showed great anticipation to cut across Roma's Kostas Manolas and poke in substitute Lucas Vazquez's close-range cross.

The Portuguese forward, who now has 13 goals in this season's Champions League, set up Rodriguez for the second four minutes later as the Colombian fired in low after a swift counter attack.

Bale comes on to improve fitness

The gap to Barcelona in La Liga has coincided with a calf injury to Gareth Bale, but, after appearing and scoring as a substitute in their 7-1 win over Celta Vigo on Saturday, the Welshman made his first start since 17 January.

The world record signing worked hard on the right wing and sent in several fizzing crosses which, had Karim Benzema been playing, might have resulted in a goal.

As it was, Real took the lead when Vasquez came on to replace Bale and set up Ronaldo with his first touch.

But it was a decent work out for the former Tottenham player, who could yet make a telling difference as the season comes to a close and will be aiming to star for Wales at the European Championship in June.

Salah the biggest threat for Roma

When Salah played at former team Basel, his manager Murat Yakin said the winger could be world class if only he could finish.

Unfortunately, that proved an accurate assessment of the Egyptian, who had a short-lived period at Chelsea in 2014, during which he was loaned to Fiorentina.

The 23-year-old caused plenty of problems for Real with his pace on the right wing, and set up Dzeko for a great early chance.

But the profligacy shown by both was further underlined with another miss by Salah after the break, and 18 minutes later Real were 2-0 ahead.

Diego Perotti's shot against the post, two minutes from time, would only have been a consolation.

'Players' reaction causes me pain'

Luciano Spalletti, Roma coach: "We are weak and at the first sign of difficulty we cannot be the team that we need to be. It is not as if Real Madrid are going through a great period of form and at the moment they are not irresistible.

"When I come back into the dressing room after the final whistle and see the players satisfied because they will get compliments for the performance, this creates a disappointment and pain in me that I cannot reconcile.

"When you go into the dressing room after a 2-0 defeat, you need to be angry and realise the chances you have thrown away over these two games."

Stats you need to know

Cristiano Ronaldo has now scored in 61 different Champions League matches; more than any other player (Raul 56, Lionel Messi 51)

Ronaldo has now scored five goals in his last six Champions League appearances against Roma.

Keylor Navas has now gone eight consecutive Champions League games without conceding, one game away from equalling Jens Lehmann's record by a goalkeeper (9 in 2005/06).

Real Madrid has 37 goal attempts, more than Roma, Gent and Wolfsburg combined.

(BBC)