In their round one final at Meadow Park, in greater north London's outskirts, the Gunners went ahead in the 19th minute after Frida Maanum took full advantage of a fumbled save by opposition goalkeeper Rugile Rulyte.
Fresh off a four-goal haul days earlier in a 6-0 thumping of Rangers, Matildas star Caitlin Foord was kept quiet on Saturday, going close in the first half but substituted off after 82 minutes along with her international teammate Kyra Cooney-Cross.
England forward Alessia Russo and midfielder Cooney-Cross both clipped the woodwork in the span of a minute after halftime, while Gunners captain Kim Little and England skipper Leah Williamson also went close.Â
Former champions Arsenal, who hovered just above 80 per cent possession throughout the contest, clung onto their narrow advantage over the Norwegians, who were surprise winners on penalties against Atletico Madrid in the previous tie.
Last year, Arsenal failed to reach the group stage after a shock defeat to Paris FC in qualifying and are under considerable pressure to do so this time around.
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Having reached the quarter-finals last year, Ajax Amsterdam were eliminated after a 1-0 loss to Fiorentina.
Benfica's hopes of repeating their run from the opening stage to the last eight remain alive after they defeated SFK 2000 Sarajevo 4-0.
Elsewhere, Paris FC beat Sparta Prague 2-0 and St. Poelten won 1-0 against Vllaznia to progress.
Celtic, Sporting Lisbon, Anderlecht and Servette also advanced, along with Galatasaray, who became the first Turkish team to get through a round in 11 seasons.
The draw for the next round's home-and-away ties will take place on Monday.
With AAP.
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