Just minutes after Bolt had cruised through the field before winding down in the closing stages and sharing a smile with Canada's Andre De Grasse, Gatlin was beaten in the final straight to end his hopes of gold.
Gatlin, who came second behind Bolt in the 100-meters final, finished third in his heat, struggling home behind Alonso Edward of Panama and Churandy Martina of the Netherlands.
The 34-year-old appeared to slow down prematurely and failed to make it through as a fastest loser after recording a time of 20.13 seconds.
"I'm happy to still be here (for the relays)," he told reporters.
"My ankle is giving me a lot of problems. I can't run properly and I had a tight turn in lane three."
While the crowd has been full of admiration for Bolt, Gatlin's presence has been less well received in Rio.
But Gatlin, who was forced to sit out during two doping bans, says he has enjoyed his rivalry with the champion in spite of the negative crowd reaction directed toward him.
"It's a showman's sport," Gatlin said.
"I think the rivalry that I have with Usain, it's turned it into a professional wrestling feel.
"Everyone's cheering for Usain, but they have someone they have to boo against."
While Gatlin stumbled, Bolt looked impressive as ever as he goes in search of a third successive gold in the event.
The Jamaican slowed down in the final stages before smiling at De Grasse's attempt to push him to go faster.
De Grasse and Bolt's exchange of warm smiles as they approached the 200m finish line spawned hilarious memes on social media.
"Strolling into the 200m final like..." read one caption.
Some thought the look demonstrated strong relationship goals. "Find someone that looks at you the way De Grasse and Bolt look at each other," said one tweet.
Another commenter thought it was "so cool" to see a heartfelt moment between the two athletes.
Maybe they could really make a go of it and travel the world together, another tweet suggested.
"He was supposed to slow down," Bolt told reporters.
"I said 'What are you doing, it's a semifinal?' But I think he wanted to push me. I was a bit lazy but I got round."
Canada's De Grasse, who won bronze in the 100-meters, came home in 19.80 seconds -- a Canadian record.
He'll be joined in the final by LaShawn Merritt of the United States, Britain's Adam Gemili, Christophe Lemaitre of France and Turkey's Ramil Guliyev.