Mikel Arteta’s side took the lead midway through the first half when Nketiah deftly redirected the rebound from a Kieran Tierney shot that came crashing off the far post past Bodo/Glimt keeper Nikita Haykin.
And Arsenal were two up shortly after as Holding nodded past Haykin at his near post from an expertly whipped in cross from Vieira that stood after a brief VAR check for a foul in the buildup.
Chasing a two-goal deficit following the break, Bodo/Glimt had more of the game in the second half, creating half-chances with Amahl Pellegrino seeing his low shot superbly saved by keeper Matt Turner in the 57th minute.
However, they still rarely threatened Arsenal with the Premier League leaders adding a third before full-time when substitute Gabriel Jesus tip-toed down the touchline and set up Viera to smash home from close range.
The two teams will meet again in Norway next Thursday for the reverse fixture, while Arsenal host Liverpool on Sunday in a savory top-flight match in England.
Arsenal lead Group A with six points from two matches, two more than third-placed Bodo/Glimt, who have played an extra game.