A quiet first half saw few chances created by either side, but Bukayo Saka eventually got the Gunners into the lead after linking well with Albert Sambi Lokonga before a ricochet from his own shot directed the ball past the goalkeeper.
The hosts had a plethora of chances to get back into the game but couldn't seem to get on the scoresheet. Amahl Pellegrino found space on two occasions but couldn't beat United States No. 1 Matt Turner, while Runar Espejord should have done much better with his finish close to the hour mark.
Mikel Arteta's tactical change that introduced Granit Xhaka saw Arsenal defend in a back four more frequently, and that looked to ease the pressure in a bright spell from the Eliteserien side to help take all three points back to north London.
A hard-fought victory forced the Gunners to be resolute under pressure from Bodo/Glimt, and they managed to grind the result that puts them into a strong position for qualification from their group in the Europa League.
A dangerous spell in the second half saw Arsenal fortunate to not concede. It is important that they remain switched on in future against tougher opposition.
Manager rating out of 10
7 -- Arteta balanced his squad astutely on the night and his substitutions were timed perfectly. The Premier League side looked as though they were losing a grip on the game after the break, but a change of shape and introduction of Xhaka made it difficult for Bodo/Glimt to get in behind.
Player ratings (1-10; 10 = best, players introduced after 70 minutes get no rating)
GK Matt Turner, 7 -- The USMNT keeper didn't have much to do in the first half, although he was also alert when the Eliteserien champions looked to play directly in behind Arsenal's defensive line. A strong stop denied Pellegrino in the second half.
DF William Saliba, 7 -- Saliba looked unfazed defensively and he had plenty of the ball as Arsenal showed patience in their attacking approach to pick their moments when to go forward. The 21-year-old also showed impressive passing range with his more direct balls into channels.
DF Rob Holding, 6 -- A mistake allowed Pellegrino to get through on goal in the first half, and Holding was slow to react at times against the counterattack, but he did make a number of clearances on a night when the opponents constantly tested him with balls in behind.
DF Ben White, 6 -- The 25-year-old didn't seem to capture the attention too much in the match, and that's normally a good thing for a centre-back. White held the defensive line well, and often made the right decision with his forward passes.
MF Martin Odegaard, 7 -- The Norway star played progressively and linked play well from midfield to help get the Gunners into some promising positions where they could play with a higher element of risk.
MF Albert Sambi Lokonga, 8 -- The 22-year-old controlled the game from midfield and rarely put a foot wrong. He picked up the assist for Saka's opener. A standout performer in Norway.
MF Reiss Nelson, 6 -- Bright down the left flank and looked to challenge his defender when in possession. Got some crosses into the box but couldn't find his intended target.
MF Fabio Vieira, 6 -- Vieira wasn't involved too much going forward, but kept things ticking in the midfield to transition the ball safely. A comfortable performance from the former FC Porto midfielder.
FW Bukayo Saka, 7 -- A positive game from the England international who troubled the opposition's defence in the first half. There was an element of luck with his opening goal, but the work he put in before the deflection saw him earn his reward. Quiet after the restart.
FW Eddie Nketiah, 5 -- Nketiah stretched the play with runs in behind, but attacks broke down on a number of occasions that could have been avoided. Isolated at times in the second half.
MF Granit Xhaka, 7 -- Anticipated play well from the midfield and helped Arsenal restore some control over the match.
FW Gabriel Martinelli, 6 -- Stretched the play down the left flank in moments when the Gunners looked to counterattack. Arsenal couldn't seem to get him on the ball enough.
MF Marquinhos, 5 -- Confident in possession but lacked cutting edge with his final ball. Wasteful too often.
DF Takehiro Tomiyasu, 6 -- Introduced at right-back and looked faultless in his 20-minute appearance.
MF Thomas Partey, N/R -- Brought in to help defend against a late push from Bodo/Glimt.