The hosts went into the halftime break with a slim 12-10 advantage on the scoreboard, but added five tries after the interval to make it two wins from two to start the URC season.
The opening exchanges were cagey but the Lions were slowly gaining the upper hand and they eventually opened the scoring in the 11th minute courtesy of a penalty from Chris Smith.
The next 15 minutes was an arm wrestle as the sides battled to gain the ascendancy, but the home side eventually increased their lead when Erich Cronje scored the opening try after Ethan Adams laid the groundwork with a barnstorming run in the build-up.
The Ospreys needed a response if they wanted something from this match and turned things around in the latter stages of the half when Keiran Williams and Efan Daniel scored well-taken tries.
Dan Edwards succeeded with one conversion which meant the match was evenly poised as the Welsh region held a slender 12-10 lead at half-time.
The second half started brightly for the Lions as their efforts were rewarded with tries in quick succession from PJ Botha and Morne Brandon.
Smith was off target with both conversion attempts, but the Lions did not have to wait long to secure their bonus point as Boeta Chamberlain then went over for their fourth try after 57 minutes.
It was one-way traffic after that as the Lions stayed true to their attacking roots and Kelly Mpeku soon crossed for back-to-back tries which meant they held a comfortable 35-12 lead by the 66th minute.
The rest of the half was frantic as both sides gave the ball plenty of air and the Ospreysâ efforts were eventually rewarded in the gameâs closing stages when Ross Moriarty scored a consolation try.
The Welsh region were reduced to 14 men in the 62nd minute when Edwards was yellow carded for a head-high tackle on Ruan Delport and the hosts made full use of their numerical advantage as they were dominant during the next 10 minutes.
Immediately after Edwardsâ departure, the home side launched an attack inside the Ospreysâ 22 and Smith delivered a cross-field kick which Mpeku gathered before crossing the whitewash.
Three minutes later, the Lions took the ball through several phases and there was great interplay between forwards and backs before Mpeku found himself in space out wide and he had an easy run-in for his seconds try.
Although Smith and Chamberlain were unsuccessful with both conversion attempts, those two tries in quick succession knocked the wind out of the visitorsâ sails and it ultimately secured the victory for the Lions.