The big-spending Principality side left it late to see off Bordeaux 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 Ligue 1'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.