The 2012 world champions were second overnight but won by a point after finishing third in the medal race.
Byrony Shaw was third in her RS:X windsurfing medal race to consolidate her silver medal.
There were also bronze medals for Alison Young in the Laser Radial and Nick Dempsey in the men's RS:X.
Poor weather caused Dempsey's medal race to be cancelled and he was placed in his overnight position.
Wales' Mills and Essex-born Clark gave British sailing a flying start with success in the opening event of the final day.
But unable to get to compete at the head of the race, their victory was only possible after New Zealand overtook the leaders Brazil near the end.
However, there was disappointment for James Peters and Fynn Sterritt with fourth in the 49ers, and it was also fourth for Ben Saxton and Nicola Groves in the Nacra 17.
British sailors Hannah Mills and Saskia Clark have won gold in the 470 Women's race on the final day of the World Cup regatta in Hyeres, France.