James Rodriguez struck a double for Monaco, while the Colombian set up Andrea Raggi for the home side's third goal as they cruised past visiting Nantes at the Stade Louis II.
While Ranieri agreed Nantes had their moments, with the struggling visitors putting seven shots on target to Monaco's four, the Italian coach was thrilled to move six points clear of third-placed Lille with six rounds remaining.
"It was a very important game tonight," Ranieri said.
"We played well even though we were in trouble on the attacks from Nantes.
"With three points won tonight, we are six ahead of Lille."
In their first season back in the French top flight, Monaco look set to finish second behind Paris Saint-Germain.
After a long season, Ranieri was impressed with how his players got the job done against a desperate Nantes side, who could have moved six spots clear of the relegation zone with a win.
"There were some difficult moments, as there have been since the start of the season," the 62-year-old said.
"But that's normal, because there are no easy games. It's not possible to play the whole season at 1000 kilometres per hour. I always say that the second half of the season is always more difficult. For everyone, except PSG.
"We played well, we scored three goals, and were compact against a good Nantes side. We were better in winning back possession. I'm satisfied."
Nantes remained 15th after the loss with 37 points, two spots and eight points clear of the relegation zone.
While Alejandro Bedoya scored a late goal for Nantes, their coach Bruno Baronchelli argued his team never looked like winning.
"I'm not happy. We can play for a hundred years like that and we'll not win ever," Baronchelli said.
"We didn't defend well enough. We weren't strong enough in the tackle.
"I get the impression that we could concede at any time, that we're going to lose. It wasn't enough."
