Having trailed by 59 points early in the third quarter, the Tigers closed to within three at the 13-minute mark of the last term.
And they looked to have taken the lead when Troy Taylor snapped the ball through shortly after, only for the umpire to award a free kick to Port Adelaide defender Troy Chaplin for holding.
The Power then steadied late in the game to win 18.14 (122) to 16.16 (112).
The result made it five victories in the seven games since Matthew Primus took over as caretaker coach.
However, most of the 37,674-strong crowd was there to see Cousins run around in the AFL for the final time, and when he entered the fray after starting on the interchange bench, the Tiger fans cheered his every move.
Although restricted by a hamstring injury, the 2005 Brownlow Medallist battled bravely to finish with 21 possessions.
He was given a standing ovation by the Richmond supporters as he ran a lap of honour following the final siren.
Earlier in the afternoon, the Tigers booted the first two goals of the match, before their skill-errors allowed the Power to take control.
The visitors capitalised by kicking 10 goals to one in the second quarter, during which Robbie Gray provided the highlight of the term when he put through a brilliant snap from deep in the forward pocket.
By the long break, the visitors were 53 points up and match seemed over.
The second half was more of a contest, but the Power held on to win their 10th game of the season.
Travis Boak ended the game with 31 possessions and best-on-ground honours, while Daniel Stewart kicked four goals.
Mitch Morton, Dustin Martin and Brett Deledio were Richmond’s most effective contributors.
Morton and Jake King both kicked three goals, while Jack Riewoldt, who had already been confirmed as the Coleman Medallist, also booted three majors, taking his season’s tally to 78.
Richmond 2.6 3.9 9.13 16.16 (112)
Port Adelaide 2.6 12.8 14.11 18.14 (122)
GOALS
Richmond: Morton 3, King 3, White 2, Post 2, Cotchin 2, Riewoldt 2, Nahas, Collins
Port Adelaide: D Stewart 4, Boak 3, Logan 2, P Stewart 2, Gray 2, Westhoff, Brogan, Cassisi, Rodan, Davenport
BEST
Richmond: Deledio, Morton, Martin, King, Tuck, White, Cotchin
Port Adelaide: Boak, Brogan, D Stewart, Cornes, Rodan, Logan
INJURIES
Richmond: Nil
Port Adelaide: Salter and Hitchcock replaced in the selected side by Pettigrew and Davenport
Reports: Nil
Umpires: Margetts, Findlay, Bowen
Official crowd: 37,674 at Etihad Stadium
