Ronaldo also played his part in the 56th opener for Karim Benzema which broke a frustrating deadlock for the league leaders at Estadio Manuel Martinez Valero.
Later his firm header after a cross by Isco extinguished any hope of a home comeback, his 29th league goal of the season.
Real, looking to take advantage of Barcelona's shock home defeat to Malaga Saturday, had been frustrated by the superb goalkeeping of Przemyslaw Tyton and some wasteful finishing with both Gareth Bale and Ronaldo left to rue first half missed chances.
Benzema, who was scoring his 19th goal of the season, also had an earlier spectacular scissor kick effort ruled out.
At the other end, Iker Casillas was making his 500th career appearance in the Real goal, but was barely troubled.
In another milestone, Carlo Ancelotti was taking charge of his 100th game for Los Blancos, who beat Schalke 2-0 in midweek in defense of the Champions League crown.
After the crushing 4-0 defeat to Atletico in the Madrid derby, Ancelotti has been delighted with the reaction of his team.
"Since the loss against Atletico, conceding four goals, we've kept three clean sheets. Team has defended well, everyone together," he told gathered reporters.
Earlier Sunday, David Moyes' Real Sociedad came from behind to secure a 4-3 win over Sevilla which lifts his side to 10th and eight points clear of the relegation zone.
Defeat leaves Sevilla trailing fourth placed Valencia by five points in the battle for Champions League qualification.
Meanwhile in the English Premier League, the race for the Champions League spots is also closing up, with Liverpool's 2-0 win at Southampton Sunday boosting its chances.
A sublime early strike from Philippe Coutinho and a second half goal from Raheem Sterling sealed three points for the visitors, who move up to sixth, but only two points behind fourth-placed arch-rival Manchester United.
Fifth-placed Southampton had two strong penalty appeals turned down but their fate was sealed when Matt Targett slipped as he tried to clear a cross and the ball fell invitingly for Sterling to score his 10th goal of the season.
The vital win lifts Liverpool above Tottenham Hotspur, who had to score two late goals to salvage a 2-2 home draw with West Ham.
Harry Kane scored an injury time penalty after being pulled down for the spot kick.
His initial effort was saved by Hammers goalkeeper Adrian but he converted the follow up.
Danny Rose had started the Tottenham fightback after goals from Diafra Sakho and Cheikhou Kouyate had left the visitors ahead with just nine minutes left to play at White Hart Lane.
The other game saw bottom club Leicester denied a valuable win as a late own goal from Matthew Upson allowed Everton to equalize for a 2-2 draw.