The Wales judoka won by an ippon to secure Britain's second medal of the championships after Colin Oates took silver in the -66kg on Thursday.
She said: "My aim was to win the Europeans, but I am happy with bronze."
Only one of the -78kg judoka can be selected for the Rio Olympics, with Commonwealth champion Powell leading the race.
There are potentially three further competitions after the Euros for either athlete to take an advantage before the Olympic qualification period finishes at the end of May.
When Powell and Gibbons had last fought at the Paris Grand Slam, Powell had won on shidos, however this time she pulled off a big throw to take the contest.
The world number nine had earlier beaten Slovakia's Anamari Velensek with a waza-ari to take her to a semi-final contest with the Netherlands' Guusje Steenhuis where another waza-ari set up victory.
The European Championships in Kazan are the last major championships before the 2016 Rio Olympic Games in August with up to 400 qualifying points on offer.
Powell and Gibbons are part of a 13-strong GB squad in Russia.
Natalie Powell beat fellow Briton Gemma Gibbons in the -78kg to claim bronze at the European Championships in Russia.