Alvarez and Koroleva finished with a combined score of 163.1913. France's Laura Auge and Margaux Chretien won gold with 169.3136 points, and Mexico's Karem Achach and Nuria Diosdado took silver at 167.7737.
The duo also finished third in the duet tech and free preliminaries on Friday and Saturday.
“We have a beautiful choreography in both tech and free, and Anita and Mariya look good together,” U.S. Senior National Team head coach Lolli Montico said. “They have improved a lot from last year.”
Alvarez and Koroleva will next compete Friday at the French Open in Paris, where they finished sixth last year.
The duo will attempt to qualify for the Olympic Games at a qualifying event in Rio de Janeiro, Brazil, March 2-6.