But that did not keep the 17-year-old Briton from finishing atop the all-around standings after the first subdivision and fifth overall with 52.831 points over the four apparatus at Olympic Stadium.
Women's qualification resumes on Wednesday with three more subdivisions. The top 24 qualify for Friday's all-around final.
"I'm really buzzing from my performance," said Tinkler.
"I've had some injury difficulties this year and have felt a bit ill this week so to have made it through today is a huge relief."
Tinkler stepped out of bounds on her third major tumbling pass during an action-packed floor routine and was equally impressive on vault where she performed two different passes.
On bars, Tinkler looked strong but counted a fall on her final release skill when she could not re-catch. She also delivered a nicely executed beam routine.
Canada's Ellie Black (55.766) leads all-around qualifying, followed by Russia's Elena Eremina (54.999) and Belgium's Nina Derwael (53.598).
Men's qualification wrapped up earlier on Tuesday and nobody could overtake Cuban 2015 silver medallist Manrique Larduet, whose Monday performance earned him an 86.699 all-around score that held up through all four subdivisions.
Xiao Ruoteng of China is in second and David Belyavskiy of Russia is in third while Ukraine's Oleg Verniaiev, who missed out on a gold medal in Rio by just 0.099 of a point, remained in fifth place heading into the men's final on Thursday.
Japan's Kohei Uchimura, who has won the last six world and two Olympic all-around titles, pulled out of qualification on Monday with an apparent lower left leg injury.
(Reporting by Frank Pingue in Toronto; Editing by Greg Stutchbury)
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