The 23-year-old halfback calmly slotted the extras after an intercept try from winger Stephen Crichton 13 minutes from time as the Panthers earned some redemption for their loss to Melbourne Storm in last year's final.
"I've been dreaming of this moment for all my life and finally it's here. We did it!," man of the match Cleary said after embracing his father, Panthers coach Ivan, on the Lang Park pitch.
"We had the hurt of last year and did it the hard way."
Souths, who stunned the Panthers 16-10 in the opening round of the playoffs, scored their second try through winger Alex Johnston eight minutes later but Adam Reynolds was unable to convert from the left touchline.
Reynolds, playing his last match for his club of 16 years before moving to the Brisbane Broncos, had a chance to tie up the scores in the dying minutes but his two-point field goal attempt came up short.
"We just kept fighting and fighting right to the end but they were just too good tonight," said the halfback, one of three survivors from South Sydney's last title-winning team in 2014.
Travel restrictions put in place to prevent the spread of Covid-19 forced the NRL final away from Sydney for the first time with the crowd restricted to 75 percent of capacity.
The Rabbitohs, one of Australia's oldest and most popular teams, had the majority of the support but it was the side from the town on the western fringes of Sydney that had the best of the early exchanges.
Cleary's sublime fifth-tackle kicks kept the Rabbitohs penned in their half and centre Matt Burton exploited the weakness in South Sydney's right-side defence to open the scoring with a try in the 17th minute.
A brilliant individual try from five eighth Cody Walker got Souths back on level terms in the 21st minute and a penalty apiece from Cleary and Reynolds had the sides locked at 8-8 until Crichton's intercept of Walker's pass.
Souths had been hoping for a record-extending 22nd Australian title, and an eighth with three clubs for their 71-year-old coach Wayne Bennett, but it was Penrith who added another triumph to those of 1991 and 2003.