The Ducks (41-5) posted four runs on five hits with a pair of hours while the Vikings (7-32) tallied two runs on five hits with one error.
The game was tied up, 2-2, heading into the sixth inning when Lindvall and Peterson both delivered for the Ducks.
Lindvall crushed a 3-1 pitch to left center, and after Koral Costa flied out to deep center, Peterson hit her own solo shot to nearly the same place as Lindvall had two batters earlier.
It was Lindvall's 10th home run of the season, the second most on the roster, and Peterson's seventh. Peterson has a team-best 51 RBIs, the fifth most in single-season Oregon history. The program record is 73 RBIs, set by Jenn Salling in 2007.
Cheridan Hawkins (25-3) picked up the win and her 25 victories are tied for the second most in the nation this year. The sophomore tossed three innings to close out the game, posting six strikeouts with no hits and no walks allowed. Hawkins dropped her ERA to 1.43 on the year.
Jasmine Smithson-Willett gave up two runs (one earned) on five hits in four innings after starting for the fourth time this season.
Oregon went ahead, 1-0, in the fourth when Janie Takeda scored on a RBI single by Costa. Portland State took the lead soon after, scoring two runs on two hits an an error in the fifth.
Hawkins came on with the bases loaded and no outs in the fifth and only the lead runner scored on a sacrifice fly. The left-hander struck out the next two batters she faced swinging.
Nikki Udria tied up the game in the bottom of the fifth. The freshman stole third and came home to score when the throw to third was booted into foul territory.
After an error let the leadoff hitter reach for Portland State in the sixth, Hawkins struck out the next three batters before Lindvall and Peterson put the game away in the home half of the inning.
Oregon hits the road this weekend, visiting Stanford for a Pac-12 series starting Friday at 7 p.m. in an ESPNU televised game. The Ducks and Cardinal will also meet at 1 p.m. on Saturday and noon on Sunday.