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British record holder Asher-Smith, 20, ran a season's best 22.37 seconds to win the 200m in Amsterdam.
Olympic and world champion Rutherford, 29, retained his European long jump title with a leap of 8.25m.
However, after missing out on the 800m final and picking up an injury, former world and European medallist Jenny Meadows, 35, said she will now retire.
Britain's defending 100m hurdles champion Tiffany Porter took bronze in a time of 12.76 seconds.
Asher-Smith is the first British woman to win the 200m at the European Championships, while Rutherford is the first man to retain the European long jump crown in 54 years.
Both athletes admitted there is work to do before they compete at the Olympic Games in Rio, which begin on 5 August.
"I'm absolutely over the moon - my first senior title," Asher-Smith told BBC Sport. "I've still got bits to work on, I got a bit tired in the last 30m.
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"Nothing really changes for me. I just want to go out there and run the fastest times when it really matters at the Olympic Games in August. My goals stay exactly the same for the summer."
Gold for Rutherford means he maintains the long jump grand slam, holding the Olympic, world, European and Commonwealth titles.
"Although 8.25 isn't very big, it's good to be the best of Europe again," he said.
"It's now about being the best of the world again. I now have five major titles and not many athletes can say that.
"If I win the Olympics in Rio, then I'll have each title in double."
Britain's Richard Kilty was disqualified from the 100m after a false start in the final, which had to be restarted.
GB team-mate James Ellington finished fifth, with the 30-year-old earlier setting a personal best 10.04 seconds to reach that stage.
Dutch veteran Churandy Martina, 32, edged French favourite Jimmy Vicaut to claim the gold medal.
There was also a memorable victory on the second day of action of the championships for Thomas van der Plaetsen, the Belgian decathlete just returning to competition after having suffered testicular cancer last year.
Britain's Dina Asher-Smith and Greg Rutherford won gold medals at the European Championships on Thursday.