Rob Flick scored the winning goal on a two-man advantage late in the second period in a penalty-filled game at the Hershey Centre.
Jordan Mayer had the Majors' first goal and Jay Gilbert added an empty-netter. J.P. Anderson made 21 saves for the win in front of a capacity crowd in Mississauga.
Andrew Shaw had the lone goal for Owen Sound. Jordan Binnington stopped 26 shots in net.
Mississauga clinched its spot in the Memorial Cup semifinal and avenged its Game 7 overtime loss to the Attack at the Hershey Centre for the OHL championship on May 15.
The host Majors get the day off on Thursday, while the Attack plays the Western Hockey League champion Kootenay Ice in a third-place tiebreaker for the other spot in Friday's semifinal.
The Quebec Major Junior Hockey League champion Saint John Sea Dogs have already sealed their spot in Sunday's final.
Mississauga opened the scoring at 8:01 of the first period. With the teams playing 4-on-4, Maxim Kitsyn made nice a pass through the Attack defence to Mayer, who wristed a shot that sneaked under Binnington's arm. The Majors thought they'd made it 2-0 at 18:27 when Devante Smith-Pelly scored, but the goal was disallowed upon review.
The Majors owned most of the play in the first, outshooting the Attack 11-3.
Owen Sound tied the game eight minutes into the second period. Matt Stanisz's point shot rebounded off the boards, and Robby Mignardi tipped it in front to a streaking Shaw who fired it home.
It was Shaw's fifth point of the tournament, tying him with Saint John's Tomas Jurco for the lead. Shaw also took four penalties in the game.
Late in the period, Owen Sound took two interference penalties on the same play, giving the Majors a 5-on-3 power play. Mississauga made the Attack pay, working the puck around to Flick who put a shot high past Binnington for a 2-1 lead at 18:24.
Gilbert added an empty-net goal at 19:25 to seal the victory.
The game wrapped up the round-robin portion of the tournament.NOTES:
Attack centre Joey Hishon sat out his second straight game with a concussion ... The Majors revealed the banners for their 1935 and 1945 Memorial Cup championship teams in a pre-game ceremony.