Four-time European champion Asher-Smith secured her first individual world medal in 10.83 seconds.
Jamaica's double Olympic champion Fraser-Pryce took her fourth 100m world title in 10.71secs while the Ivory Coast's Marie-Josee Ta Lou was third.
Reigning Olympic champion Elaine Thompson came fourth.
Asher-Smith had qualified second fastest but had to work hard in the final 20 metres to ensure she took silver.
It was also Great Britain's 100th medal at the World Championships since it started in 1983.
But it was another embarrassment for the IAAF with the Khalifa International Stadium virtually empty for the final.
The 23-year-old Asher-Smith now turns her attention to the 200m, with the heats in Doha on Monday, and she is favourite to win gold.
Meanwhile, Holly Bradshaw suffered heartbreak in the pole vault as she came fourth.
The 27-year-old, who was dropped by her sponsors at the start of the year, cleared 4.80m – a centimetre short of her personal outdoor best – but failed at 4.90m trying to remain in the competition, which was won by neutral athlete Anzhelika Sidorova.
The GB mixed 4x400m relay team of Rabah Yousif, Zoey Clark, Emily Diamond and Martyn Rooney also finished fourth in the final of the new format.
The USA took the title with Allyson Felix winning a record 12th World Championships title.
Earlier, Zharnel Hughes overcame his 100m disappointment by reaching the 200m semi-finals.
Hughes, who came sixth in the 100m final, clocked 20.24s while Adam Gemili ran a season's best of 20.06s.
He beat defending champion Ramil Guliyev in his heat and Miguel Francis also looked impressive, running 20.11s to progress.
Gemili failed to get beyond Saturday's semis in the 100m and afterwards tweeted a picture of the photo finish in his race, calling the result into question, after he came third but admitted it was rash.
"It was a bit of the heat of the moment, I should have taken 10 minutes and calmed down," he said.
"Someone showed it to me as I was getting on the bus and I went back to see the photo finish but they didn't let me in.
"It's one of those things, after watching it properly it was a tough one to call and I guess they made the right decision. These are the guys in charge of the sport.
"I have to park it, it was a bit of an angry tweet. I tried to word it in a nice way but it was pure emotion."
New 100m world champion Christian Coleman had withdrawn with soreness after his victory on Saturday night.
Gemili added: "It's another athlete. He did fantastic on Saturday and was a class apart from everyone else but the 200m is a completely different race. It makes it easier, it's one less person to run against."
Elsewhere, Elliot Giles, Kyle Langford and Jamie Webb were all eliminated in the men's 800m semi-finals and the USA's Christian Taylor won triple jump gold.