Nketiah, yet to start in the Premier League this season, grabbed his second goal in two European appearances.
Then defender Holding, who has been on the pitch for just two minutes in the league this term, headed a second before Vieira tapped in a late third to make it two wins from two for Mikel Arteta's men in Group A.
Glimt had stunned Roma 6-1 in the group stage, and knocked out Celtic, on their way to the Europa Conference League quarter-finals last season.
But their evening in north London did not get off to the best of starts when their bus got stuck on a tight bend in the narrow streets surrounding the stadium, forcing the players to get off and walk the rest of the way.
But once the match started it was Arsenal who were strolling to a comfortable victory.
Vieira should have given them the lead in the ninth minute after Granit Xhaka, one of three starters who also began Saturday's win over Tottenham, fed the overlapping Kieran Tierney down the left.
Tierney's cut-back found Vieira 12 yards out but the Portuguese midfielder's shot grazed the crossbar.
Nketiah had already curled an early effort narrowly wide before he opened the scoring in the 23rd minute.
Gabriel Martinelli did well to hold onto the ball in a congested midfield before eventually smuggling it out wide to Tierney.
The full-back launched a first-time drive which clattered the far post and fell to Nketiah to sweep into an unguarded net.
Holding doubled Arsenal's lead four minutes later with a far-post header from Vieira's in swinging cross.
Xhaka almost made it three but his curling free-kick was tipped over by Glimt keeper Nikita Haikin.
The industrious Vieira curled a shot wide before half-time and Xhaka forced a fine save from Haikin seconds after the restart.
Arsenal's new back-up goalkeeper Matt Turner had been a spectator for the first half but he was alert enough to make a fine reflex save early in the second to keep out Amahl Pellegrino's snap-shot.
Nketiah blazed a late chance over before substitute Gabriel Jesus fed Vieira for the 84th-minute goal his performance deserved to set up Premier League leaders Arsenal nicely for Sunday's visit of Liverpool.