The Paris Saint-Germain striker now has 64 goals, two more than Ronaldo and 13 behind Pele, who heads the list with 77, according to the count by world governing body FIFA.
Brazil coach Tite was reluctant to compare his current star with past greats.
"It's unfair making comparisons," he said after the match.
"What I can say is Neymar has this unpredictability. He is the bow and the arrow, he's a player who both makes and takes chances. And he gets better and better, and more mature.
"Each generation has its own merits. Ronaldo was extraordinary, Rivaldo was extraordinary, Romario and Bebeto as well, each one in his own time.
"He has the ability to get the ball in the most relevant areas of the pitch and he uses his creativity from there. He doesn't juggle with the ball. He dribbles to create danger, to unbalance his defender. That is his top characteristic as a player."
On Tuesday, Neymar equalled and then surpassed Ronaldo with two penalties either side of half-time before grabbing No. 64 in injury time at Lima's National stadium.
The PSG star later paid tribute to Ronaldo, known as O Fenomeno -- The Phenomenon -- on Twitter.
Neymar, 28, now has four career hat tricks in all competitions with Brazil, the same amount as Lionel Messi with Argentina. Prior to turning 29, Cristiano Ronaldo had only scored two international hat tricks.