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.
Basel were almost caught out by a brisk Real counter-attack four minutes into the second half, but James Rodriguez's teasing cross cross from the left flashed across the face of the goal.
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 equalise 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 their eight-game unbeaten home record come to an end.
