Although the Rabbitohs share 22 competition points with the Dragons and Panthers, their commanding win gave them a far better points differential. So they will stay kings of the castle for at least 24 hours until Penrith play the Roosters.
Souths were superior in so many areas at ANZ Stadium, their victory coming off the back of a magnificent night's work to winger Jennings, who spoiled his brother Michael's 250th NRL game, and a brace to fullback Alex Johnston.
Halves Adam Reynolds and Cody Walker were also on song as the Bunnies piled on seven tries in the space of 33 minutes after trailing 14-6.
The four-try haul by Jennings had many scurrying for the record books only to find that eight Souths players have scored five tries in the one game – the most recent was Johnston against Penrith in round 17 last year.
In truth the winning margin would have been inflated further if Reynolds had as much success with his goalkicking [four from eight] as he had with his attacking plays.
The Rabbitohs have now slammed seven straight wins in the middle of the season for the first time since 1994. Things were going so well, skipper Greg Inglis was rested with 10 minutes left to play.
The Eels were in touch at halftime, trailing by just two, 16-14. But five tries in the second half consigned Brad Arthur's men to a 12th defeat for the year and erased the spark that emerged from the 20-14 win over the Cowboys last weekend.
Jarryd Hayne scored a consolation try in the 67th minute and Josh Hoffman another in the 74th but fans had begun heading to the exits before then.
The lead changed four times in the opening 40 minutes as the Jennings show unfolded.
Proceedings started in the best possible way for Parramatta with a try to Hoffman off a Corey Norman kick in just the third minute, helped by a fumble from Souths winger Hymel Hunt.
But then disaster struck with a mix-up between Hoffman and Manu Ma'u from the kickoff, resulting in a scrum for South Sydney 10 metres out. Robert Jennings got his scoring started with a try in the left corner to put Souths up 6-4.
Six minutes later and Eels winger George Jennings scored in the right corner for the home side to take back the lead 8-6. The gap was extended when Bevan French supported a Peni Terepo run to the line.
Then Robert Jennings scored his second, followed by Alex Johnston, and the Rabbitohs were back in front 16-14. From there it was a procession and Robert Jennings scored another two tries in the second half to give him 12 from 13 games.