The British duo, who have both secured places at the Rio Olympics this summer, finished with a score of 444.48.
The pair's latest medal comes after their silver at the European Championships and bronze at the World Cup in Brazil.
Meanwhile, compatriots Tonia Couch and Lois Toulson took gold in the women's 10m synchro in Sheffield.
European silver medallists Alicia Blagg and Becky Gallantree won the title in the women's 3m synchro, while Ross Haslam and James Heatly also claimed gold in the men's event.
Tom Daley and Dan Goodfellow won gold in the 10m synchro on the opening day of the British Diving Championships.