Durham (27-31) is 4-3 on a 10-game road trip.
Walter Young delivered the big blow in the fourth inning with a bases-loaded double to left-center to make it 7-1.
Ottawa starter John Maine (4-4) made it hold up by striking out a season-high 10 Bulls in 6.2 innings.
Durham did hit two homers off Maine.
Bulls' catcher Kevin Cash and outfielder Jeff Deardorff each hit their fifth home runs of the season.
Durham now has 80 homers this season, second in the league.
Pitcher Jason Phillips, knocked out in the nine-run fourth, took the loss and fell to 2-3.
Durham looks for a split of the series Monday against Ottawa at 11:05 a.m. as John Webb meets Dave Borkowski in a battle of righties.
Coverage of this game can be heard on Triangle Sports Talk 1090 and 1490 beginning at 10:45 a.m.
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