Runners-up to Lyon last year, a fourth successive victory in this season's competition would have seen Emma Hayes' side through Group A with two games to spare.
However, they were forced to settle for a point at Estadio Alfredo di Stefano after Guro Reiten's penalty, which cannoned in off goalkeeper Misa Rodriguez, cancelled out an earlier effort from Caroline Weir.
Paris Saint-Germain leapfrogged Madrid to second place in Group A following a commanding 4-0 victory over Vllaznia, whose elimination was subsequently confirmed.
Kadidiatou Diani scored twice while Ramona Bachmann and Magnaba Folquet were also on target for PSG, who will be through with victory over Madrid when they clash at Parc des Princes next week.
Elsewhere, two-time champions Wolfsburg are the first side through to this season's quarter-finals after an entertaining 4-2 win over Roma.
Ewa Pajor's brace, which took her group-stage tally to six goals, sandwiched strikes from SveindIs Jonsdottir and Lena Lattwein, ensuring efforts from Andressa Alves Da Silva and Sophie Roman Haug were merely consolations for Roma.
The German side's 11th last-eight appearance in as many continental campaigns was confirmed after St Polten failed to beat Slavia Praha in the other Group B encounter.
The Czech outfit netted their first goal of the campaign through Kristyna Ruzickova, but Mateja Zver's free-kick means they can no longer qualify for the knockout phase.
Emma Hayes' team knew a draw would suffice as they targeted first place on Thursday, but they ultimately enjoyed a routine outing as James added to Sam Kerr's first-half stunner.
Kerr fired into the top-right corner from 20 yards out to hand Chelsea the lead, before James added two well-taken finishes as the Blues finished their group-stage campaign with an unbeaten record.
In the group's other game, Real Madrid bowed out on a positive note as Teresa Abelleira scored twice in a 5-1 rout of Vllaznia, with Scotland international Caroline Weir also on the scoresheet.
In Group B, meanwhile, two-time champions Wolfsburg clinched top spot by thrashing Austrian side St Polten 8-2 away from home, with eight different players netting for the visitors.
Roma will join Wolfsburg in the quarter-finals after wrapping up their campaign with a 3-0 victory at Slavia Praha, with Valentina Giacinti, Beata Kollmats and Elena Linari scoring as the Italians finished one point behind the German giants.
Emma Hayes' Blues sealed their place in the last eight with a comfortable 4-0 victory over Albanian outfit Vllaznia, with goals for Sophie Ingle, Fran Kirby, Katerina Svitkova and Maren Mjelde.
That proved enough to secure top spot in Group A as they qualified for the knockout rounds with a game to spare alongside PSG, at Madrid's expense.
Elisa de Almeida and Kadidiatou Diani struck to help the French side inflict a 2-1 loss upon Las Blancas, with Claudia Zornoza's late effort in vain as they crashed out of Europe.
Elsewhere, doubles for Benedetta Glionna and Manuela Giugliano saw Roma cruise past St Polten in a 5-0 rout after shrugging off an early weather delay.
That also saw the Italian side through to the quarter-finals, though they may have to settle for second in Group B, with Wolfsburg still at the summit despite a goalless draw with Slavia Prague.
The 2021-22 runners-up Barcelona will take on Roma in the last eight, while Paris Saint-Germain play Wolfsburg and Bayern Munich come up against Arsenal.
The first legs are scheduled for March 21 and 22, with the return fixtures a week later.
The semi-final draw was also made on Friday, with the winners of PSG and Wolfsburg set to face the winners of Bayern and Arsenal, while the winners of Lyon and Chelsea will go up against the winners of Barca and Roma.
Eindhoven will host the final on June 3.
Trailing to a Lea Schuller header from last week's first leg, Frida Maanum fired in a sensational 20-yard effort to level up the tie within 20 minutes of Wednesday's return game.
Stina Blackstenius powered in a header six minutes later to give Arsenal the lead in the tie for the first time in front of the 21,307 watching spectators in north London.
Jonas Eidevall's side missed chances to kill off the tie, but they saw out the victory to set up a meeting with the winners of Thursday's tie between Paris Saint-Germain and Wolfsburg.
Barcelona earlier booked their spot in the semi-finals, where either Chelsea or Lyon await, with a commanding 5-1 win over Roma at Camp Nou sealing a 6-1 aggregate victory.
Two-goal Fridolina Rolfo scored either side of Maria Leon's curler to put Barca, who finished runners-up to Lyon last season, out of sight before half-time.
Asisat Oshoala tapped in a fourth a minute after the restart and Patricia Guijarro headed in from a corner to complete the rout.
Competition debutants Roma registered a couple of attempts on target in the remaining 40 minutes, but it was plain sailing for Barca in their quest for a second European crown.
