Bozanic and Dario Lezcano put the host two goals up at the interval and, although Mario Gavranovic pulled one back in the 59th minute, Bozanic's second of the game swiftly re-established the two-goal cushion before substitute Pedro Henrique's last-gasp consolation.
Lucerne climbed to fourth spot as a result. It was Bozanic's second double in as many weeks, after he netted twice in a 4-2 loss against Aarau last weekend.
Young Boys continued its perfect start - but had to come from two goals down to see off FC Thun 3-2.
The host headed into the game with two wins from its first two games but looked to be on the way to losing its 100 per cent record when first-half goals from
But half-time substitute
The win moved
In the day's other game,