Mears and Robinson-Baker collected bronze together in the 3m synchro at the Edinburgh leg of the World Series last weekend as Britain won three medals in total.
Olympic bronze medallist Tom Daley stole the show with gold in the 10m platform while Alicia Blagg and Rebecca Gallantree took silver in the women's 3m synchro.
However a far smaller team has travelled to Moscow for the Russian World Series leg with Mears and Robinson-Baker the only Brits in action on day one.
And, having scored 392.91 to win bronze in Edinburgh, they could only record 383.46 in Moscow to place fourth and miss out on bronze to Mexican duo Yahel Castillo and Daniel Islas.
Castillo and Islas finished with a total of 399.60 as Illya Kvasha and Oleksiy Prygorov of Ukraine edged out Chinese pair Kai Qin and Chong He for gold.