The Tigers slumped to their worst start to a season in 16 years, falling behind early when they conceded the first five goals in the Power's 13.12 (90) to 6.12 (48) victory at the MCG on Saturday.
Maurice Rioli took a spectacular mark on Logan Evans' back and converted his set shot for Richmond's first goal 20 minutes into the second term.
But it was one of few moments of joy for Adem Yze's side in a fourth consecutive loss in the new campaign.
Port (2-2) squared their season record, rebounding from a horror home defeat to West Coast with an improved team display.
It could come at a cost, with Willem Drew to be scrutinised over a sling tackle on Steely Green, whose head hit the ground in the incident.
Zak Butters (30 disposals), Darcy Byrne-Jones (26) and Kane Farrell (24) were all key contributors, and Aliir (18 intercepts) gleefully mopped up loose balls in the back half.
"Aliir led the way off the back of a week of being challenged," Carr said.
"After the loss last week, having one of our leaders stand up under pressure and lead the way was what we needed, and he did that."
Mitch Georgiades, Jack Lukosius, Jason Horne-Francis and Jack Whitlock kicked two goals each for Port.
Recalled veteran Ollie Wines had 11 touches in 55 per cent game time in his first appearance of the season.
"He came in and played the role that we wanted him to," Carr said.
"He won some contested footy, and his seniority and calmness around the group was what we needed, especially in those times when the game was going against us."
Port shook off an untidy start and led by 34 points before Rioli rose high at the city end to spark a three-goal run for the Tigers leading into halftime.
But their momentum halted when Richmond ruck Samson Ryan struck Jordon Sweet about 80 metres off the ball, resulting in a free kick that Corey Durdin converted from the top of the goal square.
Yze was pleased with Ryan's attempts to make up for the blunder, but lamented the costly incident.
"You can't defend behind undisciplined acts," Yze said.
"I'll cop it if it's an execution error and we're just not as good as them, but when it's something like that they can just crush your spirit.
"He just came in then and apologised for it."
Up by 27 points at the final change, Port kicked three goals in as many minutes early in the last quarter to end the Tigers' resistance.
Midfield pair Jacob Hopper (22 disposals, eight clearances) and Tim Taranto (20, six) battled away for Richmond, who last lost their opening four games in Damien Hardwick's first season as coach in 2010.
Teenaged Tigers Sam Lalor and Liam Fawcett kicked two goals each.
