Tedesco scored one, set up another and played an important role in a further two as the Tigers ran riot in the six-tries-to-four rout.
He turned the game on its head when he created something out of nothing - stepping off his left foot and then his right to leave Alex Johnston, Kyle Turner and Sam Burgess clutching at air to score and make it 12-4 in the 19th minute.
When he sent Chris Lawrence over six minutes later with a crisp, flat pass, the Tigers were making metres at will and the Rabbitohs looked rudderless.
Inglis' try just before the break gave Souths a sniff of a chance but Tedesco again turned provider after the break, putting David Nofoaluma through a hole as they ran 90m to score through Mitchell Moses.
The Tigers' post-Farah era was off to a flying start with Tedesco, Nofoaluma, Aaron Woods and Moses all outstanding as they played with flair and confidence.
Winger Moses Suli also scored a double on debut but was found out in defence during Inglis' try.
Tigers centre Jamal Idris had an indifferent return to the NRL, dropping the ball with his first touch.
Farah, in his first outing in new colours after his controversial exit from the Tigers, largely had an uneventful night as his side were overawed.
The Rabbitohs have big problems with Inglis under an injury cloud and halfback Adam Reynolds expected to miss the next three weeks with appendicitis.
Inglis will go for scans on Saturday but said he didn't believe the injury was serious.
Souths coach Michael Maguire defended his decision to leave his strike weapon on the field for over 50 minutes playing on one leg.
"I've got some very good staff and they were obviously in conversation with Greg right throughout the game," Maguire said.
"Greg felt it was actually getting better and he could stay out there. There was a point in the second half when we thought it was no longer worth pursuing so we pulled him off."
Tigers coach Jason Taylor paid tribute to Tedesco, saying his running game would play a big part in their game plan this year.
"I didn't think he was going to score that try, it was just his brilliance," Taylor said.
"Those guys taking the line on was important tonight. Guys like Mitchell Moses, Luke Brooks and James Tedesco just being prepared to get tackled, I thought that was a key factor for us tonight and sometimes they didn't get tackled and created something for us."
Wests Tigers 34 (Luke Brooks, Chris Lawrence, Mitchell Moses, Ava Seumanufagai, Moses Suli, James Tedesco tries; Moses 5 goals) South Sydney Rabbitohs 18 (Bryson Goodwin 3, G Inglis tries; Goodwin goal) at ANZ Stadium.
Referee: Chris James, Ashley Klein.
Crowd: 16,976