Nadal, bidding for his ninth title at Roland Garros, hunted down Robby Ginepri during a first set that ended 6-0 in the Spaniard's favour.
The American greeted his capture of the first game of the second set with a clenched fist of mock celebration but defeat, while somewhat delayed, was inevitable as he folded 6-0 6-3 6-0.
Dark horse Kei Nishikori was the first top 10 seed in the men's or women's singles to miss out on the second round, the ninth seed from Japan losing 7-6(4) 6-1 6-2 to Slovakia's Martin Klizan.
The start of play was delayed for about one hour, and Maria Sharapova managed to finish off fellow Russian Ksenia Pervak for the loss of only three games on the Philippe Chatrier show court before rain returned to stop play for another hour.
Djokovic was leading 4-1 at the time and, on the resumption, broke Sousa to love. He then recovered from 0-40 on his own serve to wrap up the first set with two crushing first serves.
Rain began to fall again with the Serb, who is strongly fancied to end Nadal's hold on the title, preparing to serve for the set at 5-2. Djokovic sat, looking slightly ridiculous, in a white hooded waterproof jacket as the umpire decided whether to take the players off court.
Djokovic made a series of faces at the camera before inviting a ball boy to share his seat, and a soft drink. They chatted under a large umbrella to the amusement of the crowd.
When play resumed after five minutes, they shook hands politely before resuming their previous roles.
"It was a nice, fun time, something unusual for the grand slams," said Djokovic.
"We waited for around 10 minutes in the pouring rain on the court, so I felt there's something I should do and make a new friend. He accepted the offer to sit down, which I didn't think he would do. So he's very spontaneous little boy, and I hope I see him my next match."
Djokovic, who beat Nadal in the Italian Open final in Rome this month, also criticised the state of the court after several days of rain in the French capital. During his match, the players' first serves kicked up sprays of wet clay.
"The court is not in great shape at the moment, balls get heavier, and the more difficult it is for you to move, to penetrate the shots. Everything becomes slower," he said, "so it is more effort on your body."
Nadal, playing on the Court Suzanne Lenglen, was held in check by world No.279 Ginepri for several games in the second set but his relentless power and attritional accuracy from the baseline proved too much for the wildcard.
"Obviously coming from Tallahassee Challenger no one is hitting like that," Ginepri told reporters.
The last few games were played in weak sunshine but the forecast is for further periods of rain during the first week of the second grand slam of the year.
BLOWN KISSES
The warmup on Philippe Chatrier featured seventh seed and 2012 champion Sharapova in fetching pink and Pervak in what looked like army camouflage trousers and jacket.
Winner of the Stuttgart and Madrid claycourt titles, Sharapova went on the attack early, moving her left-handed compatriot around the court to break at the first opportunity.
But a wild volley at the net, with the whole court open, allowed Pervak to break back before the four-times grand slam champion emerged with a 4-1 lead and took the set in 27 minutes.
Sharapova broke early in the second set and won 6-1 6-2 to show she had recovered from her thrashing by Ana Ivanovic in the third round in Rome.
"It's good to play the first match and hopefully you'll be able to finish the match today with the weather conditions being as they are. It's always nice to get through," said Sharapova.
Slovakian ninth seed Dominika Cibulkova, the Australian Open runner-up, beat France's Virginie Razzano 7-5 6-0.
There were also wins for seeds Sabine Lisicki, last year's losing Wimbledon finalist, Flavia Pennetta, the winner at Indian Wells this year, and Australia's Sam Stosur who thrashed Monica Puig of Puerto Rico 6-1 6-1 despite playing with stitches in her leg following an accident in the gym last week.
Nishikori, coached by 1989 Roland Garros champion Michael Chang and tipped as one of the dangermen in the draw after an impressive claycourt season, crumbled to defeat against Klizan after serving for the first set at 5-3.
The injury-prone Japanese said he had not been able to practise enough after retiring in the Madrid Open final where he had been leading Nadal.
"It really sucks, I have to say. It's tough for me, but I guess this is my tennis life. I have to take care of my body and injury will come again, for sure," Nishikori said.
Miloslav Mecir, the son of the 1988 Olympic gold medallist of the same name, was knocked out by Tobias Kamke of Germany 7-5 7-6(2) 7-6(1) in his first match in a grand slam, after coming through the qualifiers.
