22-year-old Asher-Smith ran 10.85, a new national record for the GB star and also the joint-fastest time in the world this year.
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"I am absolutely over the moon,” Asher-Smith said after the race.
“To run a 10.8 in the championships is a big deal.
I knew was in great shape but anything can happen as you can see with the upsets this morning.
“I am so happy right now."
Gina Luckenkemper of Germany (10.98) took silver, while Dafne Schippers (10.99) completed the podium.
Hughes followed Asher-Smith’s lead when he took the men’s event with a championship record time of 9.95 with GB team-mate Reece Prescod just one-hundredth of second slower in second.
Jak Ali Harvey (10.01) of Turkey denied GB a sweep of the podium, with Chijindu Ujah’s season best time of 10.06 good enough for fourth.

Zharnel Hughes of Great Britain celebrates winning the Gold medal and Reece Prescod of Great Britain celebrates winning the Silver medal in the Men's 100 metres final during day one of the 24th European Athletics Championships at Olympiastadion on August

Image credit: Getty Images

"I am happy and the job is done,” Hughes said after the race.
I felt a bit of cramp so I don't think I could have gone any faster but I'm just happy.
"Reece Prescod is a fast finisher so I knew I had to stay relaxed as he would challenge me towards the end. I am happy that we came out victorious."
It is the first time Britain have been able to boast both the men's and women's champion at the same edition in the 84-year history of the Championships.
With additional reporting from Reuters
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