Eddie Nketiah also scored in the 2-1 victory away at Zurich in September
Striker Eddie Nketiah reacted to poke in the opener after Kieran Tierney's powerful effort came back off the post.
Fabio Vieira crossed it in for Rob Holding to head in a second before the Portuguese made it 3-0 late on.
Mikel Arteta's side have won four successive matches in all competitions and top their Europa League group, as well as leading the Premier League.
They looked like a team playing full of confidence in the first half despite Arteta making eight changes from the side that beat rivals Tottenham in the weekend's north London derby.
Nketiah, who also scored in the 2-1 victory over Zurich in September, came into the team and was a threat throughout.
He deserved his goal when he pounced on the rebound from Tierney's strike - he had curled it inches wide earlier and teed up Vieira for his effort which struck the crossbar within 10 minutes.
Vieira was also hugely impressive, coming close on several occasions as well as providing the quality service for Holding's goal and scoring himself when he finished off a scintillating move by Gabriel Jesus.
Captain Granit Xhaka had a free-kick tipped over the bar and another shot saved by goalkeeper Nikita Haikin as Arsenal could easily have added to their tally.
Norwegian side Bodo/Glimt grew into the game in the second half and posed a threat but Arsenal goalkeeper Matt Turner was not tested enough and they lacked a clinical edge.
There were signs though that Arsenal will need to be at their best again when they travel to Norway for a second meeting next week, as Arteta demanded more consistency afterwards.
"I'm really happy with the win, six points and a clean sheet. But we lacked connection between the players, we lacked consistency and domination throughout the game," he told BT Sport.
"There were eight changes, you could feel that. In the final third we looked very dangerous, the goals we scored were good.
"A few players, you could see they had a different intensity, not enough exposure in terms of minutes, so we had to make changes."
With two wins from as many group games so far, Arsenal now top Group A by two points over PSV Eindhoven, who they face on 20 October.
Summer signing Fabio Vieira scored and assisted in his second start of the season
This is a competition which Arsenal are more than capable of winning and Arteta might need to use his squad wisely to navigate it while still competing at the top end of the Premier League.
It was positive, therefore, to see strong displays in the first half from a number of players fighting for a regular place in the starting XI.
Vieira, who Arsenal signed from Porto for £34.2m in the summer, was handed just a second start and took his chance well, picking up an assist and a goal.
Victory was all but wrapped up by half-time with Arsenal fully in control but Arteta did not hesitate to make changes when their intensity dropped and Bodo/Glimt began to create a few chances.
Substitutes Martin Odegaard, Jesus and Bukayo Saka injected energy into Arsenal's play for the second half and it helped them get over the line with ease.
Jesus also delivered a moment of quality when he danced past several defenders to tee up Vieira to make it 3-0 with six minutes of normal time left to play.
The performance not only gave Arsenal a fourth successive victory but helped to carry their winning momentum into Sunday's league game against Liverpool at the Emirates.
-- Courtesy of BBC Sport