The prolific forward helped himself and the club to historic marks en route to victory.
Cristiano Ronaldo scored the only goal of the game as Real Madrid beat Basel to equal the club record of 15 consecutive victories.
The prolific Portugal forward matched Real legend Raul's tally of 71 UEFA Champions League goals with a first-half strike at Jakob-Park on Wednesday, which ensured Carlo Ancelotti's side won Group B.
Ronaldo's latest goal was his 26th in what is proving to be another outstanding season and helped Real match the run of wins achieved in the 1960-61 and 2011-12 campaigns.
Gareth Bale struck by the crossbar in the second half and Ronaldo missed a great chance to register his 72nd Champions League goal, which would have left him two adrift of new record holder Lionel Messi.
Real was not at its brilliant best, but it will take some beating as it attempts to defend its European crown, while Basel heads to Liverpool for its final group game next month needing to avoid defeat to progress.
Keylor Navas was handed a Champions League debut as Iker Casillas dropped to the bench and Ancelotti also made three changes to his defense, with Alvaro Arbeloa, Fabio Coentrao and Raphael Varane replacing Daniel Carvajal, Marcelo and Pepe.
Derlis Gonzalez, Mohamed El Nenny and Fabian Schar came into the Basel starting lineup at the expense of Matias Delgado, Marcelo Diaz and Yoichiro Kakitani.
The Swiss champion did not allow Real to settle as the game started at a frantic pace, and it took Ronaldo 20 minutes to have his first sight of goal, letting fly with his left foot from a tight angle but shooting straight at goalkeeper Tomas Vaclik.
Basel showed plenty of endeavor, but it was behind 10 minutes before the break when Karim Benzema surged forward and cut the ball back from the byline to give Ronaldo the simple task of slotting home from close range.
The host responded, and Gonzalez must have been relieved to be flagged for offside when he somehow failed to hit the target from inside the six-yard box after Shkelzen Gashi had picked him out.
Basel almost was caught out by a brisk Real counterattack four minutes into the second half, but James Rodriguez's teasing cross cross from the left flashed across the face of the goal.
Vaclik got down to his right to keep out a long-range free kick from Ronaldo as Real started firing on all cylinders following a disappointing first half.
Gashi appealed for a penalty after he cut inside and unleashed a shot which appeared to strike Sergio Ramos on the hand before flying over the crossbar, but referee Milorad Mazic signalled for a corner.
Breel Embolo then had a great chance to equalize after 66 minutes when he raced into the penalty area, but Navas did well to narrow the angle and turn the ball behind for a corner.
Bale almost sealed the points 16 minutes from time, but his thunderous strike came back off the crossbar, then Ronaldo spurned a golden opportunity to add his second goal when he side-footed wide after the Welshman had set him up.
The game was halted when a number of fans came onto the pitch before Ahmed Hamoudi wasted a great chance in time added on, as Paulo Sousa's side saw its eight-game unbeaten home record come to an end.