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The second-seeded Swiss, who is two shy of Wayne Ferreira's record of 56 consecutive grand slam appearances, never looked in danger on Court Philippe Chatrier, wrapping it up with an exquisite backhand winner which arrowed down the line.
Once again, the 17-times grand slam winner is not the top favourite on the Paris clay, but it has no impact on him.
VIDEO: French Open - day 1 - highlights
"Like the other years, they said Djokovic was going to win the four grand slams in a row, that Rafa (Nadal) was a favourite to win the tournament. Then he says it's not true. It's always the same thing every year," Federer, who won his only Roland Garros title in 2009, told a news conference.
He will face another qualifier, Indian Somdev Devvarman, for a place in the third round.
Federer, who made his grand slam debut at Roland Garros in a four-set defeat against third seed Pat Rafter in 1999, served 10 aces and fired 11 forehand winners in an 80-minute masterclass against a fresh-faced opponent who won seven consecutive tournaments this year on the Futures circuit.
The Swiss was aware that Carreno-Busta's 166th ranking in the world did not reflect the Spaniard's talent, especially on clay, so he applied the pressure early on against a player who reached the semi-finals at this year's Portugal Open.
"He had played a lot of matches on clay, in comparison with me," said Federer.
"I knew it could be tricky if I didn't sustain a certain level of play and certain aggressiveness, get caught up maybe in long rallies, maybe what he's looking for.
"I think I started all three sets well, was able to get in the lead. And then playing from the lead against a player like him it's always easier, and so I put a lot of emphasis on that."
The 21-year-old Carreno-Busta broke once in the opening set but struggled to make a contest of the match which was his first in a grand slam main draw compared to the 291 Federer has now contested at the majors.
Carreno-Busta is now set to compete more at Tour level, having played only nine ATP matches in his career to Federer's 1,101.
"I think I played eight Futures this year and I played really well," Carreno Busta told a news conference.
"I won seven, and it was very, very good for my confidence and for my level in tennis. But I think now is time for me to play these matches with these opponents."
Results from the first day of the French Open, the second Grand Slam tournament of the year, at Roland Garros on Sunday:
Men's singles
First round
Andreas Seppi (ITA x20) bt Leonardo Mayer (ARG) 6-7 (4/7), 6-4, 6-3, 6-7 (2/7), 6-4
Blaz Kavcic (SLO) bt James Duckworth (AUS) 6-2, 6-2, 6-2
Milos Raonic (CAN x14) bat Xavier Malisse (BEL) 6-2, 6-1, 4-6, 6-4
Michael Llodra (FRA) bt Steve Darcis (BEL) 6-4, 4-6, 6-1, 6-4
Kevin Anderson (RSA x23) bt Illya Marchenko (UKR) 6-3, 7-5, 6-4
Joo Sousa (POR) bt Go Soeda (JPN) 6-1, 6-3, 6-2
David Ferrer (ESPx4) bt Marinko Matosevic (AUS) 6-4, 6-3, 6-4
Roberto Bautista (ESP) bt Gilles Muller (LUX) 6-3, 6-4, 6-2
Jeremy Chardy (FRA x25) bt Benjamin Becker (GER) 6-4, 6-2, 7-5
Gilles Simon (FRA x15) bt Lleyton Hewitt (AUS) 3-6, 1-6, 6-4, 6-1, 7-5
Jan Hajek (CZE) bt Denis Kudla (USA) 6-2, 5-7, 6-0, 6-4
Sam Querrey (USA x18) bt Lukas Lacko (SVK) 6-3, 6-4, 6-4
Somdev Devvarman (IND) bt Daniel Munoz (ESP) 6-3, 6-3, 7-5
Roger Federer (SUI x2) bt Pablo Carreo (ESP) 6-2, 6-2, 6-3
Women
First round
Caroline Garcia (FRA) bt Yulia Beygelzimer (UKR) 6-3, 6-4
Anastasia Pavlyuchenkova (RUS x19) bt Andrea Hlavackova (CZE) 4-6, 7-6 (7/5), 6-4
Petra Cetkovska (CZE) bt Olga Puchkova (RUS) 6-0, 6-2
Mallory Burdette (USA) bt Donna Vekic (CRO) 6-3, 6-4
Dinah Pfizenmaier (GER) bt Mandy Minella (LUX) 7-5, 6-1
Virginie Razzano (FRA) bt Claire Feuerstein (FRA) 7-6 (8/6), 6-4
Ana Ivanovic (SRB x14) bt Petra Martic (CRO) 6-1, 3-6, 6-3
Monica Puig (PUR) bt Nadia Petrova (RUS x11) 3-6, 7-5, 6-4
Shelby Rogers (USA) bt Irena Pavlovic (FRA) 6-3, 6-4
Sabine Lisicki (GER x 32) bt Sofia Arvidsson (SWE) 6-3, 6-4
Yulia Putintseva (KAZ) bt Ayumi Morita (JPN) 6-2, 6-3
Sara Errani (ITA x5) bt Arantxa Rus (NED) 6-1, 6-2
