The Portugal forward, top scorer in the competition this season with 13 goals, netted for the sixth time in three games in all competitions by finishing off substitute Lucas Vazquez’s cross at the near post after 64 minutes.
Four minutes later Ronaldo, who put Real on the way to a 2-0 win in the first leg of the last-16 tie with a stunning strike, released Rodriguez with a delicate pass and the Colombia forward prodded the ball between the legs of keeper Wojciech Szczesny.
"It was a difficult game even though some people didn’t expect it would be, but in the end we achieved our objective, which was to go through, and we didn’t concede a goal,” Real coach Zinedine Zidane told a news conference.
Real's Keylor Navas kept his sixth straight Champions League clean sheet to move ahead of former Manchester United stopper Edwin van der Sar with the second-longest run in the competition without conceding a goal and is now unbeaten in 540 minutes.
Roma coach Luciano Spalletti said before the game that he was "asking for the impossible" from his side as they looked to overturn the deficit surrendered at the Olympic Stadium, but they had two clear chances to take the lead before the break.
Edin Dzeko and Mohamed Salah were each through on goal but shot wide of the near post. In the second half, Navas rushed out to deny Roma defender Kostas Manolas and then went flying to his right to claw away a stinging low strike by Diego Perotti.
“We had our chances and we had to score them. If we had it would have changed our mentality and the game,” Roma coach Luciano Spalletti told a news conference.
"We have thrown away a great chance because Madrid are not in great form, their football is not irresistible.”
Real's Costa Rica keeper Navas has yet to let in a goal in this season’s Champions League and only trails German Jens Lehmann, who went 853 minutes in Europe's elite club competition without conceding for Arsenal.
Roma's Egypt forward Salah missed another chance at the near post in the second period while the game was still goalless, but Ronaldo showed no such mercy at the other end.
The 31-year-old, who scored four times in the second half on Saturday in a 7-1 La Liga mauling of Celta Vigo, fired past a helpless Szczesny after an excellent piece of skill and cross by Vazquez, before teeing up Rodriguez to finish off the Italians.
(Editing by Ken Ferris)
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