The third-seeded Swiss matched Jimmy Connors's professional era (since 1968) mark despite hitting some wayward shots against the world number 78 on Court Suzanne Lenglen.
Federer, looking to secure a record-breaking 17th Grand Slam title at Roland Garros, cantered through the first set and broke decisively in the 11th game of the second, wrapping it up with a forehand winner in less than two hours.
"They are never easy, those first rounds," the Swiss world number three said. "I missed a few too many shots but I was in the lead so I could afford to do those."
Asked about matching Connors's record, Federer said he had not been aware of it before the match.
"But I'm very happy, because Jimmy Connors was a huge champion, still is, so it's a great pleasure," he added.
"That (record) is a big one, because (it means) longevity. I have been so successful for such a long time and to already tie that record, (at) 30 years old is pretty incredible, so I'm very happy."
Next up for the former world number one is
It was, however, a far from perfect performance for Federer, who hit 47 unforced errors and wobbled on his serve.
"They're never easy, those first rounds. Last thing you want is to go down a set or getting in a tough situation, but I was able to stay ahead in the first set, had bits of ups and downs on my serve," Federer explained.
"But overall I'm happy I'm through. That's what I look at in the end. Sometimes you have to come through when you're not playing your very best.
"I missed a few too many shots but I was always in the lead and could afford to do those."
Kamke certainly did not get intimidated by his opponent and foxed Federer at times with some bold shots.
"I was hitting particularly a lot with my forehand today," said Federer. "He was going there often, which is unusual because usually players go into my backhand. It was a bit unusual."
Looking ahead, Federer said there was one record he would particularly cherish.
"The absolute title, that's Connors. 109 (titles), I'm at 74 now," he said.
"Is it possible for me to equal Connors' title? 110, that would be a round figure. That would be incredible. But that's a dream. I go year after year and we'll see."
The Serbian was dragged into a first-set tie-break, which he won 7-3, before he gradually outpaced the world number 97 with a string of thundering winners.
Instead of trying to deflect all the pressure and attention that has been building up towards his title bid, Djokovic chose to embrace a sentiment voiced by tennis great Billie Jean King.
"Pressure is always present, and the way I look at it, it is a privilege and it's a challenge," Djokovic said. "So you need to try to understand and learn how to deal with it, and if you feel pressure, that means that you're doing something that is right.
"So I'm happy - I'm happy to be where I am at this moment."
Djokovic, who could meet Federer in the semi-final in a rematch of last year's epic last-four tie, is taking a down-to-earth approach to his quest.
"It doesn't give me an extra negative pressure. I really think it's a challenge and something to embrace and to enjoy," he said. "I'll try to go step by step."
Starace put up a decent fight in the opening set and was only broken in the fifth game of the second before Djokovic, who did not face a single break point throughout, found his stride on a sun-drenched Court Philippe Chatrier and raced home in just over two hours.
Djokovic next faces