Former national champion Gardner clocked 10.79 seconds to win her semi-final of the 100 metres, and Nelvis paced a high quality women's 100m hurdles field in 12.34 seconds in a first round race.
Tyson Gay and teenager Trayvon Bromell rode over-the-allowable winds to impressive times in the men's 100m semis.
Bromell clocked a windy 9.76 seconds for the top time with former world champion Gay the winner of the second semi in 9.79 seconds, also wind assisted.
"It felt good, it felt relaxed," said Gay, who is bidding to compete in his first world championships in six years.
The finals of the men's and women's 100m were scheduled for later on Friday with the top three finishers in each event qualifying for August's world championships in Beijing.
Gardner posted the fastest allowable time of the year but she was not the fastest in the women's 100.
Gusting winds pushed Tori Bowie (10.72) and Carmelita Jeter (10.76) to faster times but the wind on their race, 3.2 metres per second, was above the 2.0 mps allowed for record consideration.
(Reporting by Gene Cherry in Eugene, Oregon; Editing by Peter Rutherford)
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