During the first of three laps of the run, Bozzone led the way with Bockel just seconds behind, while American Kevin Collington worked his way into contention. Bozzone picked up the pace to open up 48-second lead in the second lap as the American moved passed Bockel.
The Aucklander showed real speed in the final lap to set a new course record.
"I am so excited to be on top of the podium. I'm pumped to get my first race of the season done with a win,'' Bozzone said.
"It was not the usual pancake flat course you expect in Florida with hills on the bike and run. I am really pleased with how the day unfolded and where my fitness is at. I feel that I have strong base to grow on through the season and am looking forward to seeing what the rest of the year has in store.''
He will return to his base in Los Angeles before taking on the ITU Long Distance World Championships in France next month and target the Ironman 70.3 World Championships in Las Vegas in September.
Fellow Auckland athlete Callum Millward finished eighth while another Aucklander, Jo Lawn, finished third in the women's race.
Results, Ironman Florida 70.3:
Elite men: Terenzo Bozzone (NZL) 3:45.51, 1; Kevin Collington (USA) 3:47.12, 2; Dirk Bockel (GER) 3:48, 16, 3. Also: Callum Millward (NZL) 4:01.39, 8.
Elite women: Mary Beth Ellis (USA) 4:14.03, 1; Mandy McLane (USA) 4:19.10, 2; Jo Lawn (NZL) 4:20.51, 3.