The 23-year-old clocked 10.83 seconds but could not match Fraser-Pryce, who stormed to her eighth world title in 10.71. Marie-Josee Ta Lou (Ivory Coast) finished third in 10.90.
"I worked so hard for this, for this championship, and hopefully I'll go on to do bigger things," Asher-Smith told BBC Sport.
When I stood on the line I was thinking right, this is your time to go. A PB, a national record - that is more than you can ask for in a final. Shelly-Ann did a fantastic performance and that's why she's an absolute legend. I am happy!
I am a clean athlete, says Hassan
In another embarrassment for organisers, the medallists conducted their lap of honour in a deserted stadium as already disastrous attendance figures hit new lows.
Asher-Smith had already made history after a season’s best 10.87 in her semi-final saw her become the first British woman to reach a world 100m final.
But it was Fraser-Pryce who always looked the favourite after cruising through the early rounds and so it proved, with the 32-year-old exploding out the blocks and storming to victory.
Asher-Smith, a three-time European champion from Berlin last summer, now turns her attention to the 200 metres, with the heats getting underway on Monday.
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