The Welsh judoka, who missed out on a medal at Rio 2016, won the second European bronze medal of her career.
Powell, 26, beat Slovenia's Klara Apotekar in the quarter-final to go through to the semi-final on Saturday.
She lost to world number one Guusje Steenhuis, however, before overcoming Stevenson to take home bronze.
On Friday, Alice Schlesinger came through the repechage to win bronze in the -63kg at the European Championships in Poland.
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The Israel-born Olympian collected her fourth European bronze after France's Clarisse Agbegnenou, a silver medallist at Rio 2016, pulled out through injury.
Schlesinger, 28, beat Poland's Karolina Talach in her opening bout, but then lost to Germany's Martyna Trajdos.
She regrouped to beat Italy's Edwige Gwend on her way to third.
"It feels good to win another European medal and this time for Great Britain," Schlesinger said.
"I have only had one competition this year due to injury, so it was good to have some fights and get back into things."
Meanwhile, team-mate Amy Livesey (-63kg) lost in the last 16 against Agbegnenou despite a spirited performance, with her opponent taking the contest by ippon.
On Thursday's opening day, Britain did not win any medals as Bekky Livesey (women's -57kg), Ashley McKenzie (men's -60kg), Chelsie Giles and Kelly Edwards (both women's -52kg) missed out.
Great Britain's Natalie Powell won -78kg bronze at the European Championships in Poland by beating Karen Stevenson of the Netherlands.