The cutter deployed the smaller inflatable chase boat, but as that vessel approached the panga with its blue light flashing, the panga veered toward it at high speed and struck it before fleeing.
Horne and another crewman were thrown into the water.
Another Coast Guard vessel stopped the fleeing panga and detained two suspects.
Asked whether any drugs were found, Coast Guard spokesman Adam Eggers said he could not immediately comment.
Smuggling boats carrying drugs or illegal immigrants from Mexico have been ranging farther and farther north along the California coast.
"Our fallen shipmate stood the watch on the front lines protecting our nation, and we are all indebted to him for his service and sacrifice," said Admiral Robert J. Papp, Coast Guard commandant.
Napolitano said the tragedy was a reminder of the dangers men and women in uniform face daily while protecting the nation. She said her thoughts and prayers were with Horne's family and all Coast Guard personnel.