The pair started slowly but were second by halfway, and a strong finish took them to 420.42 points and their third consecutive World Series silver.
China's Cao Yuan and Xie Siyi (458.82) led from start to finish.
Earlier, Britain's Tom Daley and Dan Goodfellow won bronze in the 10m synchro event.
The Olympic bronze medallists scored 406.38 to finish behind China's Aisen Chen and Hao Yang (462.57) and Germany's Patrick Hausding and Sascha Klein (408.54).
British Olympic champions Chris Mears and Jack Laugher won silver in the 3m synchro event at the Diving World Series in Kazan.