A goal at the death from Layvin Kurzawa salvaged three points for les Rouge et Blanc to keep their hopes of challenging for the Ligue 1 title alive
Two goals from Prince Oniangue looked to have secured the visitors a point after Valere Germain and Jeremy Toulalan had twice put les Rouge et Blanc in front, but Layvin Kurzawa tapped home in the dying seconds to claim a vital win for the hosts.
Ranieri was understandably delighted to have secured the three points to keep the pressure on Ligue 1 leaders Paris Saint-Germain - particularly as he did not believe his side played to their potential.
"Luck of champions? Yes, I agree. This is the truth," the Italian told BeIn Sport after the match.
"It was a very difficult game, but Reims are a very good, solid team, who played very well. I don't think they deserved to lose because they played a great game.
"My team played very well at the start. Afterwards, we were too stretched. Reims played some good football and showed themselves to be very compact.
"Before we scored the goal, it was a poor game. It's good to win this kind of game because when it finishes, you can tell yourself you didn't play that well."
Monaco's win moves them to within two points of PSG ahead of the champions' clash with Toulouse on Sunday.