Fabinho, Anthony Martial and Nabil Dirar were on target at the Stade Auguste Delaune as Monaco stretched their league unbeaten run to five games.
The win leaves them four points behind Marseille, who occupy the final UEFA Champions League qualification place.
And, with Monaco only six adrift of league leaders Paris Saint-Germain, talk of a first league title since 2000 cannot yet be discredited.
But Ferreira Carrasco said: "We started the match well and scored two goals. Then it was Reims on the attack, we suffered a bit but were able to score the third goal when it was necessary.
"The first thought is to go for third place, after if there is a way to do better, we'll see."
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