Five different Hawks earned RBIs in the win, and leadoff batter Shawon Dunston went 4-6 at the plate.
First baseman Jacob Rogers added a solo home run in the seventh, the team's first of the season.
Overshadowing the performance at the plate was starting pitcher James Pugliese, who threw five innings, striking out seven and allowing just three hits.
Three other Hawks pitchers combined with Pugliese to hold Eugene to four hits in the game.
Boise faces Eugene Saturday and Sunday before returning home for Monday's home opener against Salem-Keizer.