The Rabbitohs, trailing 16-4 with four minutes left, scored two tries before scrum-half Adam Reynolds nailed a pressure conversion to send the game into extra time.
Souths worked the play downfield before fullback Inglis kicked the 30-metre drop goal to send the Tigers slumping to a fourth straight loss.
The Rabbitohs lost England Test forward Sam Burgess with a strained medial ligament which could mean up to a month on the sidelines, while another Englishman, Gareth Ellis, limped off for the Tigers with a suspected fractured foot.
League leaders Melbourne Storm on Friday celebrated the re-signing of international scrum-half Cooper Cronk with a six-try 34-22 romp over Wayne Bennett’s Newcastle Knights to continue their unbeaten start to the season.
And Canterbury Bulldogs joined Brisbane Broncos in joint second spot after a 30-20 win over the Gold Coast Titans on Sunday.
Brisbane withstood a second-half comeback to down St George Illawarra 28-20 at home on Friday. A long-range drop goal from Todd Carney six minutes from time gave Cronulla Sharks a 15-14 win over the Penrith Panthers.
The Sydney Roosters upset last season’s grand finalists New Zealand Warriors 26-8 in Sydney to move into the top eight. Parramatta star Jarryd Hayne powered the Eels to their first win of the season with a 29-20 upset of defending champions Manly Sea Eagles on Saturday.