An own goal in injury time from substitute John Arne Riise left Liverpool stunned and Chelsea dreaming of Moscow.
Liverpool had led from a first-half goal by Dirk Kuyt and looked to be heading to Stamford Bridge next week for the second leg of this Champions League semi-final in pole position.
But although Liverpool had created most of the scoring chances in a captivating match, Chelsea will know that their priceless away goal could be decisive as they aim for the May 21 final.
Beforehand it had all been about the powerbrokers in the directors' box.
Liverpool co-owner Tom Hicks' presence may well have concerned Merseyside Police, but it was never going to be a low-key visit. The Texan arrived in the city to head straight for the club's Melwood training complex.
He chatted with manager Rafael Benitez and watched training from the restaurant balcony before eventually heading to Anfield, arriving almost three hours before the game. Despite predictions, there was no police escort.
The Dubai International Capital delegation - who had stayed in Chester overnight - of negotiator Amanda Staveley and chief executive Sameer Al Ansari arrived with less fanfare and sat quietly away from the owners.
Chief executive Rick Parry was relegated by the Hicks entourage from his usual front-row seat to way back in the box, where he was able to watch Hicks and son Tom jr waving their scarves and singing along with the fans.
So much for the sideshow. There was a vibrant match in store, and with three England managers watching as well. Fabio Capello, Steve McClaren and Sven-Goran Eriksson were as spellbound as the rest at a packed Anfield.
Liverpool fielded the side that had beaten Arsenal in the previous round, with Chelsea having Frank Lampard, Michael Ballack and Didier Drogba back.
And they started full of desire and pace, unfazed by the vociferous Kop, who had pointedly ignored the Hicks showboating.
Ballack and Lampard were dominant and Liverpool were instantly forced back, fussy Austrian referee Konrad Plautz doing nothing for the flow.
Liverpool needed to raise their game, and they did when Xabi Alonso's ball sent Kuyt away, Petr Cech half stopping the effort before Ashley Cole belted it away.
But Chelsea were playing the football and Joe Cole should have done better from a Lampard chipped pass.
Steven Gerrard was being smothered by Claude Makelele everywhere he went. But one clipped pass from the Liverpool skipper after 31 minutes sent Fernando Torres clear, only for Cech to produce a vital save.
But Liverpool's steady improvement was to produce a goal after 42 minutes. And it was all about Kuyt, with his seventh goal in 11 European ties this term.
After his run and cross preceded a poor clearance, he won the ball back from Lampard and when it was turned into the box there was Kuyt to force it under Cech's despairing dive.
That gave Liverpool all the incentive they needed to return after the break flying forward looking for another; Ryan Babel tormenting Paulo Ferreira and Gerrard and Alonso at last finding space.
Babel surged into the middle and unleashed a fierce right-footer that curled just wide.
Liverpool then lost Fabio Aurelio after an hour, collapsing with what looked like a recurrence of his groin problems. Riise sprinted into the fray.
Salomon Kalou then came on for Joe Cole, Chelsea searching for a way back into the game. Ballack's header was held by Jose Reina and Jamie Carragher got in the way of Kalou's close-range shot.
The balance was swinging again, Drogba a constant threat. Liverpool sent on Yossi Benayoun for Babel with 15 minutes left, referee Plautz still enraging Liverpool with almost every decision.
Carragher's stunning tackle on Lampard stopped an almost certain goal, Liverpool now living on their nerves as Chelsea surged forward.
Cech made a fine save to stop Gerrard's dipping volley, Nicolas Anelka coming on - eventually - for a very reluctant Ballack.
Torres, who had a tough time against John Terry and Ricardo Carvalho, lost control when put clear by Gerrard.
Terry was booked for a body-check on Javier Mascherano in injury-time, and Cech saved superbly again from Torres.
But the sucker punch was to come. In the fifth minute of time added on, Riise dived forward in the six-yard box to head a Kalou cross into the roof of his own net, under pressure from Anelka.
The Kop were stunned, Chelsea delirious, somehow they had achieved the away goal and draw they desperately wanted.
