Parry went close twice in quick succession as Southport continued to be put under pressure and Chris Lane was booked for a foul on Michael Rose after 35 minutes.
Stephenson, who made a choke sign at the Heat during last year's playoffs, then was the subject of a flagrant foul from now-former Heat backup Dexter Pittman later in that series, drove the lane with 3:05 left in the third period and drew a hard foul from Battier.