The result was largely expected after the Norwegian champions humiliated Klaksvik 3-0 in the UEFA Champions League, with Nigerian striker Victor Boniface scoring a hat-trick in his UCL debut.
The forward put the home side in front 11 minutes into the first leg encounter.
Boniface went close to increasing Bodo/Glimt’s lead several times.
The former Flying Eagles striker was rewarded for persistence one minutes after the half hour with a brace.
The Nigerian grabbed his hat-trick two minutes before the hour when he fired home from the penalty spot.
Thus, the Norwegian team have a very good advantage ahead of the return match on 12 July.
The winner will meet Linfield or New Saints in the next round.