Former Central Coast Mariner Bozanic has been in prolific goalscoring form since joining Lucerne, after recent doubles against both FC Zurich and Aarau.
Young Boys made it four wins from four at the start of the new season with a 3-1 victory at FC Zurich.
First-half goals from Alexander Gerndt and Michael Frey put Young Boys in charge and, after Zurich had pulled a goal back through Alain Nef just before the hour mark, the visitor wrapped up the scoring and the win with a 90th-minute third from replacement Yuya Kubo.
Pacesetter Young Boys, the only side still boasting a 100 per cent record, is now three points clear of second-placed Lucerne.
In the day's other game, Aarau salvaged a point from its trip to Thun thanks to a 90th-minute equaliser from Davide Calla.
Calla had given Aarau the lead with a fourth-minute penalty but goals from Benjamin Luthi (10) and Berat Sadik (27) turned the game Thun's way before Calla's late heroics saw the spoils shared.