Real, already qualified for the last-16, chalked up their 15th successive win in all competitions although they had to survive a difficult second half against the Swiss champions who refused to go quietly.
Despite their defeat, Basel, who have six points from five games, can still qualify for the last 16 if they avoid defeat at Liverpool in their final match.
Messi set a Champions League scoring record of 74 goals when he netted a hat-trick in Barcelona's 4-0 win at APOEL Nicosia on Tuesday to surpass the record of 71 he jointly held with former Real Madrid and Schalke 04 striker Raul.
Ronaldo pulled level with Raul's total when he scored from close range after Karim Benzema got to the byline and pulled the ball back in the 35th minute, Real's first genuine chance of the match.
It was the 12th consecutive Champions League away game, including last season's final, in which the Portuguese has scored.
Real coach Carlo Ancelotti said he believed Basel had the edge over the English Premier League side for the match at Anfield.
"They're in better shape than Liverpool at the moment, they are in very good physical condition," he told reporters. "At this moment Basel have a slight advantage."
"They caused us some problems in the second part. We fought hard and that's why we won."
Basel lost 5-1 at the Bernabeu but seemed uninhibited as they created a series of chances during the second half.
Shkelzen Gashi fired over from a good position after Fabian Frei threaded the ball through to him and the Albania forward was guilty of a poor finish again when he shot weakly at Keylor Navas from the edge of the area.
Gashi then sent a looping header over the bar from the edge of the area while Navas did well to save from Breel Embolo as the teenager tried to go around him.
Real were always dangerous though and Gareth Bale fired against the underside of the crossbar before a Ronaldo shot grazed the post.
