Coleman smashed Maurice Greene's 20-year-old world record last month by clocking 6.34 seconds and he came within 0.03 seconds of that at Arena Birmingham.
The American, who turns 22 on Tuesday, never looked in danger as he beat Su Bingtian of China by 0.05 and U.S. teammate Ronnie Baker by 0.07. Other world indoors records tumbled: American Kendra Harrison set a new mark in the 60-meter hurdles as did compatriot Sandi Morris in the pole vault, and New Zealand's Tomas Walsh in the shot put.
It was a third world indoor silver medal for David Storl of Germany. He and Tomas Stanek of the Czech Republic threw 21.44 but Storl had a superior second best throw.
America was favored to sweep the podium in the 60 hurdles and although Harrison and Christina Manning finished one-two respectively, Nadine Visser of the Netherlands edged Sharika Nelvis for bronze.
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There was another American one-two in the women's 400. Courtney Okolo controlled from the start and won in 50.55 seconds. Teammate Shakima Wimbley moved ahead of Britain's Eilidh Doyle on the final straight to finish second.
Morris attempted to break the world indoor pole vault record but failed in three attempts at 5.04 meters.
She was runner-up at the 2017 world championships and 2016 Olympics, plus at the previous world indoors.
Morris finally got her hands on a gold medal when she broke the championship record with her third attempt at 4.95, although she faced an anxious moment with one more woman left in the competition.