The English side beat their hosts 5-1 at the Groupama Stadium, with Caitlin Foord and Frida Maanum handing Arsenal a 2-0 lead before Melvine Malard halved the deficit.
Foord scored again in between two goals from Ballon d'Or runner-up Beth Mead to give Jonas Eidevall's side an impressive opening victory in Group C.
Barca romped to a 9-0 success against Benfica in Group D thanks to seven different goalscorers.
Asisat Oshoala and Geyse scored two each, while goals also arrived from Patri Guijarro, Aitana Bonmati, Mariona Caldentey, Ana-Maria Crnogorcevic and Claudia Pina as last season's runners-up strolled to victory.
The other game in Group D saw Bayern Munich earn a tougher three points at home to Rosengard after Loreta Kullashi's opener for the visitors was cancelled out by Carolin Simon, before Linda Dallmann struck a second-half winner for the Germans.
Group C's other contest ended with Juventus claiming a 2-0 win at FC Zurich, with late goals from Valentina Cernoia and Barbara Bonansea earning Joe Montemurro's side three points.
Jonas Eidevall's side were already assured of a place in the knockout stages, but ran riot nevertheless at Wefox Arena to ensure they would be seeded in the last eight.
Along with Maanum's treble, Caitlin Foord and Stina Blackstenius both scored a brace, while further strikes from Kim Little and Mana Iwabuchi completed the scoring.
"We scored some really good goals, and I'm happy to have got my hat-trick," Maanum told UEFA.com. "It's easier when you're surrounded by really good players. This is a nice early Christmas present, for sure!"
Arsenal were joined in the quarter-finals by Lyon, who are through to the last eight for the 14th time in 16 seasons after snatching second place in Group C with a goalless draw against Juventus.
Elsewhere, Barcelona ensured they advanced to the knockout stages as Group D winners following a thumping 6-0 victory over Rosengard.
Though already guaranteed progression beyond the group phase, Barca were in no forgiving mood as Asisat Oshoala scored twice with Mapi Leon, Fridolina Rolfo, Marta Torrejon and Irene Paredes also on target.
That took their goal tally to 29 - the highest in any Women's Champions League group stage - and meant Bayern Munich had to settle for second place despite Klara Buhl's double in a 2-0 win over Benfica.
The Women's Super League outfit preserved their unbeaten record in Group C through Vivianne Miedema's lone finish, to take a 1-0 win over the Italian giants and cement their hold on the pool.
Defeat for Joe Montemurro's side means reigning champions Lyon have vaulted them into second place after another comfortably victory over Zurich.
Melvine Malard's double was sandwiched by goals for Lindsey Horan and Delphine Cascarino in a 4-0 win, to inject further life into a campaign that saw them go winless over their first two matches.
Last season's beaten finalists Barca were meanwhile handed a first loss of the tournament, as Bayern claimed revenge for their prior loss with a 3-1 triumph.
Both sides now sit atop Group D with nine points, three ahead of third-placed Benfica, who kept pace with a 3-1 win of their own over Rosengard.
Gunners defender Frida Maanum put through her own net on the stroke of half-time to hand the reigning champions victory at the Emirates Stadium, leaving both sides on 10 points in Group C.
Jonas Eidevall's team knew they would qualify with anything less than a four-goal loss after establishing a head-to-head advantage by hammering Lyon 5-1 away from home in October.
However, the sight of a distressed Miedema leaving the field on a stretcher after appearing to catch her studs in the turf will provide cause for concern.
Miedema – the Champions League's top goalscorer in the 2016-17 and 2019-20 campaigns – has hit the net twice in the competition this season.
In Group C's other fixture, a four-goal haul from Cristiana Girelli helped Juventus profit from Irina Pando's red card in a 5-0 win over Zurich, teeing up a winner-take-all meeting with Lyon next week.
Meanwhile, Barcelona and Bayern Munich both ensured qualification from Group D, with the Spanish champions doing so in emphatic fashion with a 6-2 rout of Benfica.
Bayern joined them in racking up the goals with a 4-0 win at Rosengard, as Georgia Stanway joined Tainara, Sydney Lohmann and Julia Landenberger on the scoresheet.
