Amusan, who set the world record in the semi-finals of last year's world championships, had a provisional anti-doping suspension lifted on Thursday, but could still face an appeal that could potentially reinstate the ban.
Amusan, whose world record is 12.12, was slow out of the blocks before cruising to a time of 12.48 seconds, third fastest on the night.
"I'm just thankful I'm here in Budapest and able to race, using my talent," Amusan said. "It has not been the best but I'm here. I tried to stay as relaxed as possible (through the uncertainty) and do what my coach tells me. So here I am."
Kendra Harrison (30) of the United States blazed to a world-leading 12.24 seconds to top the heats.
"I do not really know how I did it, I was kind of blurred, I need to go back and look at it," Harrison said. "The team USA, we have the hardest team to make in the hurdles and that is what makes our event so exciting. Hopefully, we will be able to make a podium sweep."
Teammate Nia Ali (34), the 2019 gold medallist who fell in the opening round at last year's worlds, won her heat (12.55) to advance.
Amusan's presence at the global showpiece was a surprise, with her suspension lifted just two days before the meet began.
The Athletics Integrity Unit (AIU) provisionally suspended the Nigerian last month due to three whereabouts failures within a 12-month period, but the decision was overturned by the AIU's disciplinary tribunal panel.
Her announcement in Tuesday's heat received a mix of cheers with a smattering of boos.
The details of her case will be published on the AIU's website as early as Wednesday, chair David Howman told reporters. The AIU have 30 days to decide whether or not to appeal to the Court of Arbitration for Sport (CAS).
"We have some concern that it might set a precedent which will be difficult for future cases," Howman said.
"So the job we will undertake is to get an independent review of the decision, to determine whether we should consider appealing and then as a board we have to decide whether we will take that step."
The semi-finals are on Wednesday.