They scored 428.91 to come second behind Chen Aisen and Lin Yue of China.
Daley, 21, and Goodfellow, 19, improved on their effort in the first round of the series in Beijing, where they picked up bronze.
Tonia Couch and Lois Toulson took bronze in the women's event, while Chris Mears and Jack Laugher won 3m synchro bronze for Britain.
Coach and Toulson's bronze followed a silver won in Beijing, but Mears and Laugher's success was their first medal of 2016.
The third round of the series takes place in Windsor, Canada from 15-17 March before the final leg in Kazan, Russia a week later.
British pair Tom Daley and Dan Goodfellow won 10m syncro silver in the Dubai leg of the Diving World Series.