Rozee's short-term future hangs on results of scans on a suspected left hamstring tendon tear suffered in Port's 20.13 (133) to 10.10 (70) triumph on Sunday at Adelaide Oval.
The Power's new coach Josh Carr won for the first time as problems magnified for his counterpart Brad Scott.
At one stage, the inside 50m count was Port's by 21 to two.
And midway through the second term, the Bombers were 50 points down and already out.
Essendon also lost backman Mason Redman to a left knee issue and second-gamer Dyson Sharp (ankle).
The dire display followed a round-one loss to Hawthorn by 62 points, but coach Scott called for calm while retaining faith in hs players to fight.
"No one wants to hear all the preaching about stability and all that sort of stuff right now," Scott said.
"But the reality is, you've only got two options: you can give up or you can fight.
"It's difficult at the moment, because it doesn't appear to look like that (there is fight),.
"But I believe in these guys and I think they're made of the right stuff."
Power captain Rozee was instrumental in setting up victory with 21 disposals and four clearances before limping from the field in the third quarter.
Port's brilliant skipper appeared to injure his left hamstring after straining to tackle, with some reports of nerve trouble in a buttock.
"It doesn't look great," Power coach Carr said.
"Initially there was a bit of nerve damage and (he) couldn't feel his leg ... it looks likely a tendon involved.
"Fingers-crossed it's not, but that is probably the most likely scenario. It could be a significant injury."
The concern came as Rozee and vice-captain Zak Butters (36 disposals, seven clearances) were midfield forces while Aliir Aliir (19 marks) ruled in defence.
Jason Horne-Francis (26 touches) kicked three goals in Port's game-busting burst of eight majors from midway through the opening term to halfway into the second.
Jack Lukosius also kicked three majors and Joe Berry, Joe Richards, recruit Corey Durdin and Mitch Georgiades had two each.
Their collective feats easily broke any resistance from Essendon, though Jhye Caldwell (27 possessions), Zach Merrett (25), Darcy Parish (24), Nate Caddy (four goals) and Isaac Kako (1.4) battled against the flow.
After recruit Brayden Fiorini kicked the opening goal, the Power logged eight consecutive majors as Butters and Rozee pulled the strings in the midfield.
Port, with Horne-Francis slotting three successive goals in the spree, were untroubled in creating a 32-point quarter-time lead, 6.5 to 1.3.
The Power stretched their advantage to 50 points in the second term, as the Bombers' goalless span continued until a Sam Durham strike 22 minutes in.
Port held a commanding 49-point break at halftime, 10.7 to 2.6.
And the hosts rolled on with another decisive quarter in the third. Despite losing their captain, they scored five goals to three to increase their margin to 62 points ahead of a tame last quarter.
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