Dee, who shot 4-of-6 behind the 3-point line, also cleared six rebounds and handed out five assists for the Toreros (17-16), who will now appear in the second round against an opponent to be determined. Christopher Anderson registered a double-double with 11 points and a game-high 11 assists as the team had assists on all but seven of 31 field goals.
Also hitting for double figures for San Diego were Jito Kok with 14 points, Brett Bailey 13 and Dennis Kramer 12 points, to go along with nine rebounds and three blocked shots.
Portland State (17-15) was led by DaSahun Wiggins with 14 points in a reserve role, followed by Tim Douglas with 10 points as no one on the roster made more than three field goals.
The Vikings led by a basket very early on, but the team made a total of just nine field goals in the first half and shot 1-of-7 behind the 3-point line, allowing USD to take a 36-27 advantage at the break.
In the second half the Toreros pulled away with 61.5 percent shooting from the floor, including 7-of-12 beyond the arc, en route to the comfortable 22-point win at home.
San Diego finished the night hitting on 54.4 percent from the field overall, compared to only 38.2 percent for the visitors.