Rollins, who celebrates her 22nd birthday on Sunday, was last out of the blocks but had drawn level with defending champion Pearson by the ninth barrier and edged ahead of the Australian over the last to win in 12.44 seconds.
Olympic champion Pearson, who was plagued by a hamstring injury earlier in the season, finished second in 12.50.
Britain's Tiffany Porter was quickest out of the blocks and ran well to finish third in a personal best 12.55.
Pearson immediately knew she had lost her title and was the first to congratulate Rollins, easily identifiable in her red, white and blue headband and still looking at the big screen in the stadium for confirmation of the win.
Rollins came to attention in June at the U.S. championships where she won in 12.26, the fastest time run since 1992, while Pearson, who had dominated the technical event in recent years, was just returning from a second hamstring injury.
Pearson, famed for her smooth hurdling action, suffered defeats in three of her four Diamond League races this season but after finally winning in London last month was confident she could come good for the world championships.
The 26-year-old set a season's best in each of her three races in Moscow but said she was still not fully fit.
"I've never been so happy to get a race over and done with. I'm very happy with how this season has ended. It has been very, very hard," she said.
"I'm not 100 percent, these girls are, and only one girl's beaten me tonight."
(Writing by Alison Wildey, editing by Mitch Phillips)
