Needing a quick start, Chelsea missed a golden opportunity to cut the deficit in half. Ellie Carpenter's drilled cross landing right on the penalty spot where Sjokeke Nusken fired wide much to the disappointment for the majority at Stamford Bridge.
That disappointment was even more audible a few minutes later as the Blues inched ever closer to that opening goal following a wonderful disguised pass from Lucy Bronze cutting open the Arsenal backline, and finding Alyssa Thompson, though the winger was unable to find the bottom left corner.
While the hosts had started on the front foot as expected, they were not throwing constant chances at Arsenal. They wasted another good moment when Thompson played a wonderful one-two with Sam Kerr which ended in the American firing high over the crossbar.
The Gunners chances were few and far between, a thumping effort from Katie McCabe flying just inches over the upright was the closest that either side were to breaking the deadlock in the opening half of a second leg which had not managed to spring into life just yet.
The visitors started the second half on top, but Chelsea found the first big opportunity of the second half, Nusken chipping a pass through to Kerr, who was forced to delay her shot due to the onrushing Arsenal backline.
The Australian somehow managed to arrow her powerful effort towards the top corner, requiring a big hand from Van Domeselaar to keep the scores even.
Sonia Bompastor's side needed a spark because their hopes of a first Champions League title continued to fizzle out as the seconds ticked away.
A year ago, Chelsea overturned a 2-0 deficit at this stage of the Women's Champions League to lead 3-2 at half time against Manchester City. 12 months on, this was a side lacking clear quality in the attacking areas.
The home support fell silent while the Arsenal fans were cheering every touch of the ball from their team, The Gunners were growing in confidence while Chelsea's continued to diminish.
You could see it from when Chelsea sloppily gave the ball away, allowing Beth Mead to break away and dance around the Blues backline before putting in a cross that met the head of Stina Blackstenius and looped over into the stands.
The Swede thought she had ended the tie after putting a header into the bottom left corner. VAR disallowed it and gave a Stamford Bridge crowd new life, having been stunned into silence just seconds prior.
In mere minutes, the Gunners went from control to survival. Lauren James skipping past a couple of defenders before firing a curling effort which was pushed onto the post by Van Domselaar, before being smashed off the upright once more by Veerie Buurman.
Somehow she topped it moments later, getting her fingertips to a header from Nusken from point blank range. The German would pull one back with 90 seconds to play, though it was to be too little too late.
Bompastor's red card in added time summed up an extremely frustrating evening for Chelsea.
The Blues were deflated and defeated while Arsenal were still alive and kicking in their European adventure.