Layvin Kurzawa's stoppage-time goal have Monaco what could prove to be a priceless victory, after the hosts had twice been pegged back by a brace from Prince Oniangue.
The result leaves Monaco two points behind Paris-Saint Germain, with the leaders due to travel to Toulouse on Sunday, and Ranieri praised the relentless attitude his side had shown.
"My players have never stopped believing we could win it," he said.
"Until the last moments, they tried to create chances and they kept faith.
"That's why I am extremely satisfied of the mental strength and the resolve displayed by my team."
Ranieri also had praise for his opponents, who more than played their part in a marvellous spectacle, but were ultimately undone after Aissa Mandi's late dismissal for a high challenge on Kurzawa.
"When I say Reims play 'champagne' football, I really mean it," he said.
"They are always able to produce great football and to create chances. As a result, they are able to score at any moment.
"I think it was a beautiful game to watch for the fans and I am glad that at the end of the day we won it.
"It was very, very, very tough. I must admit Reims did not deserve to lose the game. A draw would have been a fairer result.
"But that's football and it is obviously good for my team, isn't it?"
