Tolman, a freshman, hit the first pitch he saw from JR Bunda into the left-field corner driving in pinch runner Nick Catalano from third, Steven Packard from second and Ryon Healy from first to give the Ducks a 4-1 lead.
Aaron Payne made it 5-1 in the bottom of the eighth when he scored on a throwing error by Portland catcher Bo Cornish after a failed squeeze play. Payne was on third after reaching base on a one-out triple.
Before Oregon (19-6) broke the game open in the bottom of the seventh, Portland (8-16) threatened to do the same thing in the top of the inning. The Pilots loaded the bases with one out and the top of the order coming to the plate, but reliever Darrell Hunter got Nick Armenta to bounce into an inning ending double play.
Hunter (2-0) picked up the win allowing one hit while walking one and striking out one in 1.1 innings. The right-hander, who was the eighth of nine pitchers for the Ducks, inherited runners on second and third with one out. He walked the first batter he faced and then got Armenta to ground out to J.J. Altobelli at short who tossed to Kevin Minjares at second who made a nice turn and got Armenta by a step at first.
Freshman Garrett Cleavinger got the final four outs, three on strikeouts, to get his second career save.
The Pilots took an early 1-0 lead with a run off Jordan Spencer, the Ducks second pitcher, in the top of the second inning. Caleb Whalen led off the inning with a triple and scored on a Brian Frattali sacrifice fly to centerfield.
Tyler Baumgartner and Graham led Oregon's 10-hit attack with both going 2-for-4.
With a league series against Washington starting on Thursday at PK Park, Oregon planned to staff the game with pitchers each throwing one inning. Brando Tessar got his first start of the season, getting the Pilots in order in the first.
Spencer, Cole Wiper, Sam Johnson, Jared Priestley and Clayton Crum all pitched one inning as well allowing just three hits between them. Derek Smith ran into trouble in the seventh forcing the Ducks to go to Hunter with just one out in the seventh.
The Ducks and Huskies open their series on Thursday at 6 p.m. at PK Park, with game two on Friday at 6 p.m. and Saturday's series finale at 7 p.m. Saturday's game will be televised by the Pac-12 Networks.