Biggar struck with seven minutes remaining in Llanelli as the reigning Magners League Champions dented the Scarlets’ fine start to the season.
The Scarlets faithful arrived in high hopes following three successive victories over Connacht, Aironi and the Dragons.
Nigel Davies’ men had scored 13 tries in those three outings but they drew a blank against their greatest rivals.
The Ospreys outscored their hosts by two tries to nil, with Richard Fussell and Alun Wyn Jones crossing in the second half after the Scarlets had led 9-6 at the break.
Superb hands from Andrew Bishop allowed Wales full back Lee Byrne to send Fusell in at the corner for the Ospreys’ first try, although the majority of the 13,700-strong crowd were convinced the final pass was forward.
New Ospreys skipper Alun Wyn Jones claimed his side’s second effort as the match swung back and forth after Shane Williams and Tommy Bowe combined well in the 58th minute.
Wales fly-half Stephen Jones kicked all 18 points for the Scarlets courtesy of six penalties as he produced an assured display just a month out from the start of the autumn internationals.
Jones had the chance to level the match with another penalty just moments left but he missed the target from wide on the right.
The result sees the Ospreys climb to fifth place in the Magners League table, while the Scarlets drop to fourth.
