The VFL Magpies led for the entire day to break Port's previously undefeated streak of 28 games.
It was Tarkyn Lockyer's second win of the season with the team now sitting just outside the top eight.
"We have played good footy over the last few weeks but have been unable to keep it together for four quarters," Lockyer told collingwoodfc.com.au after the match.
"Today we did that and I couldn't be prouder of the boys.
"Looking at the names on paper, it wasn't our best side out there today but we showed intent for the contest and won the contested footy."
Tom Young and Marley Williams controlled the midfield for most of the day with skipper Kris Pendlebury maintaining the structure down back while providing plenty of run.
After making his AFL debut and notching consecutive matches, Kirk Ugle was lively up forward booting three goals along with Irish recruit Caolan Mooney.
Collingwood will aim for its second straight win when it hosts Bendigo next Saturday afternoon at Victoria Park.
Final score
Collingwood: 5.3 7.6 13.8 15.11 (101)
Port Melbourne: 3.2 5.9 7.13 10.20 (80)
Collingwood
Goal kickers: 3 Mooney, Ugle, 2 Stubbs 2, Gault , Ceglar , Ferraro, Hahn, Farmer, Boland, Paine
Best: Young, Riddle, Williams, Pendlebury, Wallace, Ugle
Leading possession winners
27 - Williams
25 - Pendlebury
24 - Young
23 - Wallace
Port Melbourne
Goal kickers: 2 O'Farrell, Cain, Breust, Galea, Pleming, Pitt, Wooffindin, Scipione
Best: O'Farrell, Baird, Pleming, Dwyer, Noonan, Pitt
