Madrid were made to work hard in the Primera Division encounter before Karim Benzema opened the scoring in the 67th minute and Ronaldo put the result to bed late on.
The match at the Bernabeu was an emotional occasion for Ronaldo, who just hours earlier had joined with his countrymen in mourning the 71-year-old Eusebio as the Portugal legend was laid to rest in Lisbon.
A minute's silence was observed at the Bernabeu ahead of kick-off and Ronaldo was keen to highlight the important role Eusebio played in his own development.
"The goals are for Eusebio," he said. "I was very close to him and he helped me a lot.
"He is a legend for me and today is a sad day.
"We have lost one of the greatest players of all time.
"I appreciate the tribute that the stadium and Spain have paid to him. To feel the warmth of Spain and the rest of the world is very important."
Nicknamed the Black Panther, Eusebio was regarded as one of the best players of all time and helped Portugal to third place at the 1966 World Cup, finishing as top scorer in the tournament with nine goals.
He made his name at club level with Benfica, winning 11 league titles during a 15-year spell there and two Golden Boot awards as Europe's leading goalscorer.
He also notched 41 goals in 64 appearances for Portugal, part of a total of 733 goals for club and country across his glittering career.
Ronaldo is one of just two players to have scored more international goals for Portugal - Pauleta is the other - and could one day threaten Eusebio's overall tally after passing 400 career goals with his brace on Monday.
Ronaldo has now scored 20 goals in La Liga this season, taking his total for Madrid in all competitions to 230.
He also hit 118 goals during his time at Manchester United and five at first club Sporting Lisbon, while 47 of his goals have come in the colours of his national team.