The Portuguese was well below his best but struck twice late to make it 353 club strikes, a tally which also saw him surpass his Brazilian namesake.
The Portuguese was not at his best as the Blancos struggled to break down the visitors but latched on to dangerous balls from Dani Carvajal and Gareth Bale to net a double late in the game and also saw an effort ruled out for offside in the closing stages.
The 28-year-old, who is the favorite to win the Ballon d'Or next week, struck 69 goals in 59 games for club and country in 2013, and his first two this year mean he now has 400 senior strikes in his career.
The ex-Manchester United man currently shares the record for international goals for Portugal with retired striker Pauleta on 47 and has hit 353 club goals over the course of his career, a total which saw him surpass the Brazilian Ronaldo, who netted 352 in his career, on Monday.
The Madeira-born forward's 400 goals have come in 653 games for club and country but, even more impressively, the Portuguese now has 230 in just 221 appearances for Real Madrid.