The Broncos must win their last three regular-season games and hope other results go their way if they want to avoid missing the finals for a second straight year.
Brisbane struck first when Ben Hunt dabbed through a daft grubber for Justin Hodges, who was a late inclusion after recovering from a hamstring strain.
Inglis then proceeded to break the game open and the Rabbitohs went on a rampage for the rest of the first half, putting on four tries in 17 minutes.
The Rabbitohs evened it up when Inglis hit the line at pace and carried several Broncos over with him.
He then touched the ball twice for one of the tries of the year. After regathering a perfect Adam Reynolds chip, he ran over Hoffman, offloaded to Sam Burgess before backing up to score beside the posts.
Chris McQueen regathered a loose ball close to the line for a touchdown and, three minutes later, former Broncos premiership winner Lote Tuqiri snatched up the ball when Daniel Vidot fumbled a Souths bomb.
Souths carried a 24-6 lead into halftime as the Broncos botched several chances inside the Rabbitohs' 20-metre zone on both sides of the break.
Brisbane reduced the deficit to 12 when Sam Thaiday charged over.
However, they were guilty of bombing a number of prime opportunities, including one in which Vidot spilled the ball with the line open.
When Inglis crossed for his hat-trick in the 64th minute, the win was sealed before the Rabbitohs put the cherry on top with four-pointers to Luke Keary and Kirisome Auva'a.
Brisbane scored a consolation try late in the match through Jack Reed.
The Rabbitohs will have a nervous wait during the week after McQueen was put on report for a high shot on Josh McGuire and Ben Te'o was cited for a chicken wing tackle on Thaiday.
Souths coach Michael Maguire described Inglis' performance as dominant and said he was happy with how his side were building with three rounds remaining.
Inglis said he did not go into the game trying to blow the opposition off the park and praised his teammates for laying the foundation for his heroics.
"If you put in a team performance and a team effort, you come up with stuff like that," he said.
"We just have to keep doing those things for those opportunities, for those things to arise.
"Now it's back to the drawing board and we can back up again next week against the Cowboys."
Broncos coach Anthony Griffin said it appeared Hoffman had suffered a broken leg and the No.1's season was over.
When asked whether he agreed with the summation of Wayne Bennett, who will take over from Griffin next year, that Souths were predictable, the Brisbane mentor quipped: "The bloke at the back (Inglis) is a bit hard to predict."
"As you saw tonight, he can do things that no one else can do if he puts himself at the right place at the right time."
- AAP
