Jonas Eidevall's side came into their first qualifying round final on the back of a 6-0 crushing of Rangers, but on this occasion, a Frida Maanum strike was enough to seal Arsenal's progression.
The Norwegian midfielder capitalised on a first-half howler from Rosenborg goalkeeper Rugile Maria Rulyte, who attempted to punch a Caitlin Foord cross clear but only managed to palm the ball further towards her exposed goal.
Defender Mathilde Harviken tried to hack clear off the line, but Maanum was in the right place at the right time to pounce on the goalkeeper's mistake with 19 minutes played.
Eidevall's side continued to overwhelm their Scandinavian opponents, but the ruthlessness they displayed against Rangers eluded them on the night; Alessia Russo hit the frame of the goal twice and Kyra Cooney-Cross once.
Nevertheless, the Gunners banished the demons of 2023 - where they lost at this stage to Paris FC - and the draw for the second round of Women's Champions League qualifying takes place on Monday.
Arsenal can meet last year's nemesis Paris FC, Juventus, BK Hacken, Fiorentina or Sporting Lisbon in the second qualifying round, and they are one of five seeded teams in the league path alongside Manchester City, Wolfsburg, Real Madrid and Paris Saint-Germain.
Monaco 
Stade Brestois 29 
Bordeaux 
Nimes 
Bayern Munich 
FC Augsburg 
Paris Saint Germain 
Toulouse 
CSKA Moscow 
FC Rostov 
Leicester 
Chelsea 
Valencia 
Betis 
Dynamo Kyiv 
Chornomorets Odesa 
Verona 
Inter 
Bayer Leverkusen 
FC Heidenheim 
Borussia Dortmund 
SC Freiburg 
VFL Wolfsburg 
Union Berlin 
Arsenal 
Nottingham Forest 
Everton 
Brentford 
Spartak Moscow 
Lokomotiv Moscow 
Rangers 
Dundee Utd 
Atletico Madrid 
Alaves 
Lens 
Marseille 
Ingulets Petrove 
Shakhtar Donetsk 
AC Milan 
Juventus 
ST Malo 
Manchester City 
Tottenham 
Eintracht Frankfurt 
Werder Bremen 
Girona 
Espanyol 
Feyenoord 
Heerenveen 
ST Etienne 
Montpellier 
Grenoble Foot 38 
Heart Of Midlothian 
Celtic 
Reims 
Lyon 
PSV 
Groningen