Goals from Guro Reiten and Sophie Ingle sent the holders through to the semi-finals, after the two sides had contested an enthralling 2-2 draw in normal time.
City had looked to have snatched the win with five minutes left on the clock, thanks to Lauren Hemp's fourth goal in three games, but Niamh Charles' injury-time wonder strike forced the additional 30 minutes - and Emma Hayes' side capitalised on their momentum.
The defeat means City have failed to reach the semi-finals for only the second time since 2014, having won the trophy on three occasions in 2014, 2016 and 2019.
Familiar foe, the two sides locked horns for the 24th time since City entered the top flight - a tenth meeting in cup competition.
While a bright start on Sunday had set the wheels in motion for our stunning first-half thrashing of Aston Villa, it was Chelsea who threatened in the early exchanges of this well-contested encounter.
Beth England was inches away from connecting to Erin Cuthbert’s cross, while Sam Kerr could only find the side-netting inside ten minutes.
Shouts for a penalty were waved away when Cuthbert then went to ground under pressure from Lucy Bronze before the Scotland international fired over.
At the other end, City struggled to carve out clear-cut chances and the visitors made their pressure count on the brink of half-time, as Alex Greenwood’s sliced clearance fell into the path of Melanie Leupolz, who volleyed past Karen Bardsley, despite Steph Houghton’s best efforts.
Significant improvement was required in the second half and inspired by the half-time teamtalk, City were level within seven minutes of the break, courtesy of Chloe Kelly's sheer persistence.
The winger – the hosts’ best attacking threat in the opening 45 – chased down Magdalena Eriksson inside the Chelsea penalty area, dispossessing the defender before composing herself and drilling into the far corner.
As a result, the second half proved a more end-to-end affair with both sides chasing a winner.
The visitors almost hit back instantly, as Bardsley clawed Pernille Harder’s effort wide of the post.
England then headed over the bar and Kerr smashed a half-volley well wide, while Kelly almost turned provider for Hemp at the backpost, in a late flurry of activity at both ends.
Referee Richie Watkins dismissed another penalty claim when Kelly was seemingly nudged off the ball by Jonna Andersson, before Georgia Stanway fired straight at Ann-Katrin Berger.
PFA Young Player of the Year Hemp thought she had bagged a late winner, reacting quickest to a loose ball in the box and smashing home, sparking joyous scenes.
However, Chelsea levelled in the dying embers as Charles was afforded too much space and executed a stunning volley past Bardsley to send the tie to extra-time.
With the momentum, the visitors swung the game in their favour when Reiten slid into an empty net at the backpost in first-half extra-time, and Ingle made sure of the victory, rocketing an effort past Bardsley to end our hopes of a second comeback.
Hayes' side will host West Ham or Durham in the semi-finals.
HOW WE LINED UP...
Bardsley continued in goal, shielded by a backline of Bronze, captain Houghton, Greenwood and Esme Morgan with Walsh protecting the back four.