Coleman, the fastest man in the world over 100m this season, clocked 10.04sec to comfortably win his semi-final at Sacramento's Hornet Stadium.
In the women's 100m semi-finals, 2016 Olympic silver medallist Tori Bowie cruised into her final in a time of 11.03sec.
Bowie was joined in the final by Allyson Felix, who is not expected to run the 100m at the World Championships in London. Felix edged into the final after finishing fifth fastest overall in a time of 11.22sec.
The 24-year-old is desperate to make up for the bitter disappointment of last year, when she missed out on the Olympics after finishing sixth at the trials in Oregon.
Friday was Harrison's first race since breaking her hand at a meeting in Doha last month.
"I wanted to come out here and put a good number down," said Harrison, who ran with a metal pin in her left hand.
A few weeks after missing out on a place to Rio last year, Harrison smashed Yordanka Donkova's 28-year-old world record, clocking 12.20sec at a meeting in London.
Brianna Rollins, the gold medallist in Rio, is not competing in Sacramento following a one-year ban for missing three drug tests.
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