Second seed Djokovic enjoyed a 6-2, 6-1, 6-3 dismissal of hapless Dutchman Thiemo De Bakker in the first round before 16-time major title-winner Federer romped to a 6-3, 6-4, 7-6 (7/3) win over Spain's Feliciano Lopez.
Also going through on a sweltering day at Roland Garros was former US Open champion, and 2009 semi-finalist here, Juan Martin del Potro, a winner in four sets against Croatia's Ivo Karlovic.
But sixth seed Czech Tomas Berdych, a semi-finalist last year, wilted in the heat, losing in five sets to French qualifier Stephane Robert, the world number 140.
One day after his 24th birthday, the red-hot, world number two Djokovic comfortably saw off the 71st-ranked De Bakker in just 92 minutes.
Djokovic, who is likely to depose Rafael Nadal as world number one by the end of the tournament, is also favourite to snatch the Spaniard's French Open title, having seen off his rival in the Madrid and Rome claycourt finals.
His win on Monday took him to within four victories of equalling John McEnroe's 1984 record for a winning season start of 42 triumphs.
"It's my favourite grand slam, even though I haven't won it yet," said Djokovic, a semi-finalist in 2007 and 2008.
"I've been playing really well on clay. I've won three (claycourt) tournaments (Belgrade, Madrid and Rome) in the last few weeks, so I'm trying to build on that confidence," added Djokovic, whose complete winning streak has now reached 40 matches, stretching back to Serbia's Davis Cup triumph in December.
Djokovic, the Australian Open champion, who has seven titles under his belt already this year, will play either French wild card Benoit Paire or Romania's Victor Hanescu for a place in the last 32.
World number three Federer, playing at his lowest seeding in eight years at a grand slam, is taking part in his 46th consecutive major.
He had won all his previous eight matches against Lopez but would have been wary of an opponent who had a match point in their last encounter at the Madrid Masters second round earlier this month.
However, he was in little danger on Monday, cruising to victory against a player who has now lost eight times in the first round in 11 Paris visits.
Federer will next tackle French wild card Maxime Teixeira for a place in the last 32.
"It was different to Madrid, the conditions were slower and Feliciano maybe didn't get as many free points as he thought he might have done," said 2009 champion Federer.
"It was important for me to be solid on my serve from start to finish, which I was. I think I played a good match."
Argentina's del Potro overcame a first-set blip to defeat Karlovic.
Del Potro, who was a doubt for the tournament because of a hip injury, having missed the 2010 event due to wrist surgery, claimed a 6-7 (7/9), 6-3, 7-5, 6-4 win.
The 25th-seed hit 21 unforced errors to Karlovic's 42 and will next face Slovenia's Blaz Kavcic, with Djokovic a potential third round opponent.
"I'm not thinking about Djokovic," said Del Potro. "Kavcic is playing well. I'll need to play good tennis, probably better than today."
Top seed Nadal, bidding to equal Bjorn Borg's record of six French Open titles, gets his campaign underway on Tuesday against John Isner of the United States.
Berdych, a semi-finalist last year and the Wimbledon runner-up, slumped to a shock 3-6, 3-6, 6-2, 6-2, 9-7 defeat against Robert, despite having had a match point at 5-4 in the final set.
It was 31-year-old Robert's first career win at Roland Garros and just his second victory in eight grand slam appearances.
The only other seeds to tumble out on Monday were French number 22 Michael Llodra, who lost 6-7 (5/7), 6-3, 6-3, 6-3 to Belgian qualifier Steve Darcis, and Canadian 26th seed Milos Raonic.
He went down 6-4, 4-6, 6-3, 6-4 to Germany's Michael Berrer.
- AFPTags: sport, tennis, france