Rozee's sizzling 18-disposal opening quarter propelled Port to a 15.12 (102) to 8.6 (54) win on Saturday at Adelaide Oval.
The skipper finished with 36 touches, seven clearances and one goal and his vice-captain Zak Butters gathered 33 touches and also kicked a goal before being rested and substituted.
Brownlow medallist Ollie Wines (30 disposals, nine clearances, one goal) also feasted to keep Port (10 wins, six losses) in fourth spot ahead of other games.
By halftime the trio had a whopping 64 disposals and 17 clearances between them, and Mitch Georgiades kicked four goals to create a match-defining 44-point lead.
Georgiades finished with five majors and Jason Horne-Francis booted three.
Rozee fired with an instant classic of an opening term: 18 disposals at 83 per cent efficiency, five clearances and two tackles.
Butters (14 touches) and Wines (13) completed the on-ball domination, and Georgiades cashed in with two majors in two minutes to set an ominous early tone.
The Bulldogs didn't score until the 21st minute when Sam Darcy missed a set shot. Teammate Jamarra Ugle-Hagan sprayed another from just 15 metres soon after and Port led 5.2 to 0.2 at quarter-time.
Bulldog captain Marcus Bontempelli - who had only eight first-half possessions and 21 for the game - broke his side's goal drought early in the second term.
But Port remained in control with five goals to three, with Georgiades slotting his fourth on the half-time siren for a 10.5 to 3.3 scoreline.
The Dogs' woes were compounded when Aaron Naughton was substituted with concussion, the key forward hurt when blocked behind play by Brandon Zerk-Thatcher.
Port, with Horne-Francis kicking two goals and missing another set shot, extended their lead to 52 points at three-quarter-time, 12.8 to 4.4.
The Bulldogs belatedly outscored the Power four goals to three in the final term.
Bontempelli, Tim English and Rhylee West scored two majors each and Adam Treloar had a match-high 38 disposals.
But the ninth-placed Dogs could slip six premiership points outside the top eight by the end of the round ahead of fixtures against Carlton, Geelong and Sydney.
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