Aside from a brief 10-minute period just after the break that yielded one try, the Rabbitohs' pack was overpowered by their opposition and looked rudderless without suspended hooker Issac Luke.
A comeback loomed when Bryson Goodwin leaped for John Sutton's kick in the 50th minute, however Canterbury's Curtis Rona regained the momentum for his team with another signature touchdown eight minutes later.
It was the leading tryscorer's 20th of the season.
Departing second-rower Frank Pritchard set up first points for the match with a stellar 10th-minute offload for Cook, before Trent Hodkinson's looping long ball found Perrett in the 17th.
The visitors had the home side's measure in attack and defence, as evidenced by Brett Morris' trysaving tackle on Dylan Walker in the 27th minute, before latching onto another Pritchard offload a minute later.
Cook completed a flawless first half by reacting first to a Hodkinson field-goal attempt, charged down by the Rabbitohs, saving a ball well over the dead ball line for Perrett.
Alex Johnston and Jason Clark both nabbed consolation tries late in the game.
Bulldogs captain James Graham was severely concussed in the opening minute of the second half but questionably returned to the match.
Rabbitohs coach Michael Maguire said his side simply failed to mentally engage at the start of the match and were consequently blown off the park early.
"At the end of the day, it comes down to how you turn up," he said.
"Preparations are right, but they built a bit of pressure at the start, scored a couple of tries early, and then we had to work our way back into it".
Bulldogs coach Des Hasler said it was an important win given their finals predicament and the form of their opponents.
"It was one that we needed given the complexity of the eight at the moment," he said.
"Obviously they were a bit understrength, but we knew we had to turn up and be pretty determined because they're in pretty good form, Souths."
