The Real Madrid man came into the Group B meeting with Liverpool at Anfield two behind Raul's mark of 71 in the competition proper, while Barcelona rival Lionel Messi lurks just a further goal behind.
And the Portuguese forward opened the scoring midway through the first half to take his tally to 70, before a brace from Karim Benzema wrapped up a comfortable 3-0 success for the reigning champions.
Ronaldo will have the chance to at least equal Raul's mark in the reverse fixture in two weeks' time, but only after Messi has played against Ajax.
And while delighted with his first goal in six attempts, Ronaldo made it clear that the personal accolade was of secondary importance.
"It was special, it was my first goal here at Anfield so I feel very proud for that, I feel happy that we won three points... so amazing," he told Sky Sports.
"We knew before the game that Anfield is a difficult place but we played fantastic, especially in the first 45 minutes, and we deserve to win.
"I'm not worried about that [the record]. I'm going to beat his record I know, tonight or another game, me and Messi is very close too, so I'm happy because it's a good work, an indication of good work, but the best thing is that the team win, we have nine points so 75 per cent of the qualification is done."
Ronaldo scored from the spot in Real's 4-1 win over Atletico in the final of the competition back in May, and the 29-year-old believes the 10-time European champions can become the first side to win back-to-back titles since Milan in 1989 and 1990.
"Why not? We're taking it step by step," he said. "We know the qualification is the priority of the team.
"We’re going to try, like last year. We know it's going to be very tough but we are positive and I think it will be possible if we play like that."
