Benzema’s 17-minute second half hattrick saw Real Madrid progress 3-2 on aggregate, cancelling out Kylian Mbappe’s two-goal advantage for the Parisians.
The 34-year-old has thus become the oldest player to score a hattrick in the history of the Champions League and he climbed to third on the Real Madrid’s all-time top scorers list.
Courtois has tipped Benzema to become a leading contender for the prestigious Ballon D’or award this year while Ancelotti hailed his leadership qualities.
"I think he's one of the greatest players in the world, the best number nine, maybe with Lewandowski right now," Courtois told RMC Sport.
"I think he showed why he should, maybe, win the Ballon d'Or this year. He's a great player, a real captain. He led the team to victory with his goals and his class."
Ancelotti added: "Karim Benzema is a fantastic leader, a fantastic centre forward."
"I'm very happy with what he's doing and his attitude.
"After the first goal, we got into a good dynamic, we pressed and controlled the ball better. We had fewer difficulties in the second half compared to the first.
"At half-time, we said to ourselves that we had to stay in the game, even if it was difficult, thinking that something could happen.
"PSG are a great team with great players, but that's football, every little thing can change everything like that first goal."
