Sara Dabritz's goal in extra-time, which put Lyon 2-1 on aggregate had seemingly sent the hosts out after Vanessa Gilles had netted late in the second half to force the extra period.
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Then, with two minutes of injury time played at the end of extra-time, Lauren James advanced inside the box and was tripped. After a protracted VAR check, Maren Mjelde stepped up and buried her spot-kick to send the tie to penalties.
From there, Chelsea's luck held. After the sides had exchanged misses, US international Lindsey Horan saw her kick saved by Ann-Katrin Berger to put Emma Hayes' side into the last four and keep in tact the dream of an unprecedented treble.
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Chelsea's aggregate lead, won thanks to Guro Reiten's brilliant strike in the first leg in France a week ago, had almost been wiped out inside the first five minutes.
Magdalena Eriksson failed to make good contact with a clearance, and the ball fell at the feet of Signe Bruun whose fizzing drive flew inches over the crossbar to the relief of the Blues skipper.
The hosts settled, and should have taken the lead when James showed good strength in midfield and released Sam Kerr to run clear. Christiane Endler in the Lyon goal narrowed the angle well, and Kerr's early shot came back off the goalkeeper and away to safety.
James drew another save from Endler, this time a fingertip effort to keep the Blues forward from finding the top corner with a brilliant curling effort after cutting in from the left. Moments later, Kerr broke and set up Melanie Leupolz who clipped just over.
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Chelsea had had the better of the first half after weathering early pressure from the reigning European champions. Kerr and James were a threat every time they took possession in the Lyon half, and there was a palpable confidence to them as they looked to move a step closer to a first European crown.
Yet with a single-goal aggregate lead, they remained vulnerable against a side that has won this tournament on six of their last seven attempts.
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Lyon nearly levelled the tie moments after the break, and it was Eriksson again at fault. The captain dwelt too long on the ball, inviting on Danielle van de Donk who dispossessed her 18 yards from goal before losing control as she shaped to shoot allowing the Chelsea defender to recover. It was another let-off for the home side.
Their luck ran out 13 minutes from the end of normal time. Horan got in down the right for Lyon and advanced to the touchline. Her low cross was pulled back as far as Gilles, who beat the flat-footed Eriksson to the ball and turned it inside Berger's post.
Extra-time saw Hayes' side take control of the play without seriously threatening to win it in the 30 minutes. Johanna Rytting Kaneryd came off the bench and took the game to Lyon down the right wing as both sides tired, but the quarter-final looked destined by then to be won on penalties.
That was until Dabritz's decisive intervention at the end, taking a touch as Eriksson failed to cut out a cross and guiding the ball back across goal into Berger's far corner to seemingly break Chelsea hearts.
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Then, after 127 minutes of play, came James' tumble, Mjelde's leveller and Berger's heroics to put the hosts through.