The Texas-based swimmer, a 100m butterfly bronze medalist at last year's world championships, set a time of 51.41 seconds with boyhood idol Phelps second in the heat with a 51.60 that left him fourth overall.
"It feels like a morning swim. Relaxed, easy," Schooling told reporters.
Phelps has already amassed three golds at the Rio Games and has other priorities, balancing the need to qualify comfortably without damaging his chances for the evening men's 200m individual medley final.
If the American wins that event, for his 22nd Olympic gold and 26th medal, he will become the first swimmer to win the same event at four successive Games and only the third athlete after discus thrower Al Oerter and long jumper Carl Lewis.
If that fails, the 100m butterfly gives him a second chance to pull off the feat as he has also won that at the last three Games and holds the world record of 49.82.
A medal is the main aim for the day but qualifying in the second semi-final heat would have made his life easier with the IM scheduled for 11 p.m. local and the butterfly semi-finals starting at 11.34.
Phelps admitted he had messed up, even if the time was acceptable, because he now faced being in the opening semi. An odd finish number would have put him in the later group.
"I like to have those extra seven or eight minutes in between," said the American. "It’s another 300 (meters) I could do in the warm-down pool.
"Obviously in the first swim I needed to take care of business and then whatever I can do in the second one just to make it through is what I’ll do tonight."
Hungary's Laszlo Cseh, who boasts the fastest time of the year so far, was second fastest with Tom Shields of the United States third.
South Africa's world champion Chad Le Clos, who shared the 100m butterfly silver medal in London with Russia's Yevgeny Korotyshkin, was seventh.
Singapore had two swimmers in the semis with Quah Zheng Wen qualifying 16th with a personal best of 52.08.