The big-spending Principality side left it late to see off Bordeaux 2-0 on their return to the big time, with Emmanuel Riviere breaking down the hosts.
After that, marquee signing Radamel Falcao marked his debut with a goal and Italian coach Ranieri was left a happy man.
"The goals were important, but I think it's too early to talk about anything else," he told the competition's official website.
"I was very curious to see my team play against a strong side like Bordeaux, who have tough players, strong players who play a very compact counter-attacking style.
"It's a great debut for Monaco because it was our first Ligue 1 match against a big team."
Falcao was largely quiet throughout, but chipped away at his 60 million euro fee with a goal.
"This is a very important win. I think it's vital to start your league campaign with a win. Especially away from home, on the turf of a team like Bordeaux," he said.