It was the fifth consecutive international medal the pair had picked up since competing for the first time overseas earlier this year.
They won a bronze at the World Cup in Brazil in February before picking up silvers at the World Series events in Windsor and Dubai and a bronze in Beijing.
They owed their podium finish in Kazan to a stunning fifth round dive of 94.35 points, which moved them up from fifth to third.
They finished with a score of 442.59 points to finish behind China’s Yue Lin and Aisen Chen (487.67) and Ukraine’s Maksym Dolgov and Oleksandr Gorshkovozov (450.87).
Meanwhile, Goodfellow’s Plymouth Diving team-mates Shanice Lobb and Victoria Vincent were in action on the opening day of the Dresden Youth International.
Lobb finished fifth in girls’ A platform final, while Victoria Vincent, better know for her platform diving, came seventh in the girls’ B one-metre final.