Fresh from his win in Geneva last week the world number seven and three-time Grand Slam finalist looked confident on the Paris clay, serving close to 90 per cent in first serves.
Ruud, a losing finalist in the previous two editions of the French Open, earned three break points at 3-2 and more on the Brazilian's next service game before snatching a break on his seventh opportunity to go 5-3 up and bag the first set.
Alves had matched Ruud's power game for about an hour but gradually the mistakes piled up as Ruud did not give a single break point away in the entire second set.
Another early break in the third saw Ruud firmly in the driving seat and he sealed his 6-3, 6-4, 6-3 win in just under two hours.
He will face either Monaco's Valentin Vacherot or Spaniard Alejandro Davidovich Fokina in the second round
"This is one of the biggest tournaments for me and for everyone every year. One of my highlights," Ruud said.
"I’m always looking forward to it. The last two years have given me so much here in Paris. I hope I can make it another good year.
"I think it's been a good clay season for me. Madrid and Rome could’ve gone a bit better. It wasn’t what I hoped for. But other results went well. All in all I’m happy."
Ruud restores family pride at French Open after almost 30 years
In winning, Ruud restored a little family pride by beating his opponent, whose uncle once deprived the Norwegian's father of a tour title.
Up in the stands on Court Philippe Chatrier was his father and coach Christian, a former top 40 player who only reached one final in his career. That was in Bastad in 1995 when he lost to Fernando Meligeni.
"We talked about it at breakfast, actually," said Norwegian seventh seed Ruud.
"My father lost the Bastad final one time in his career, so he was never able to win an ATP tournament, and the guy he lost to in the final was Felipe's uncle.
"I think both me and my dad wanted to get some revenge on the Meligeni family. It was worth the wait, I guess. It was many years we had to wait, but we got it today."
Meligeni ended his career with a 2-0 record over Christian Ruud, also defeating the Norwegian in the second round of the US Open in 1997.
