Gatlin, who lit up Hayward Field at the weekend by clocking the world's fastest time this year en route to victory in the 100m, jogged in 20.32 seconds behind Ameer Webb at a rainswept Hayward Field.
"I just took my time, made sure I was in the top three; when the rain hits you, just play it smart. Get to the next round, get faster and rise to the occasion," Gatlin told reporters.
The most impressive display of the round came from Merritt, the 2008 Olympics 400m champion who could emulate the legendary Michael Johnson by winning the 400m and 200m in Rio de Janeiro.
Merritt, who set the world's fastest time this year on his way to victory in the 400m on Sunday, has already clocked the world's fastest time in the 200m, a blistering 19.78sec in Nassau on June 27.
The 30-year-old booked his place in the semifinals of the 200m with a time of 20.09sec.
Although it was the third quickest time of the first round, Merritt had eased up a good 20 metres from the end and clearly had plenty left in the tank as he crossed in first place.