The Reds were second best throughout the tie, despite star striker Luis Suarez enjoying a number of golden opportunities, and were punished by a quick-fire Zenit double as Hulk and Sergey Semak struck in the second half.
The Russian champions boasted a fully fit squad going into the game, with their last competitive action coming in a 1-1 league draw against Anzhi Makhachkala in mid-December.
Reds boss Brendan Rodgers, meanwhile, was without cup-tied duo Daniel Sturridge and Phillipe Coutinho, but fulfilled his promise of selecting a strong squad for the tie, with Martin Skrtel, Raheem Sterling and Joe Allen all being re-introduced after Monday’s Premier League defeat to West Brom.
Both sides raced straight out of the blocks as a fantastic opening couple of minutes provided glorious chances at either end.
First, Alexsandr Kerzhakov was denied his 12th goal of the season by Pepe Reina, before Luis Suarez displayed superb footwork in the opposite penalty area, only for the ensuing shot to flash just wide from close range.
And Reina was forced into another great save minutes later as Hulk struck from distance, the Spaniard having to use his fingertips to tip the ball inches wide of the post.
But Zenit’s early dominance could not stop the game’s next chance falling to the visitors – and it was a big one.
Nicolas Lombaerts gave possession away cheaply in his own half and Suarez capitalised, storming into the penalty area and rounding shot stopper Viacheslav Malafeev. The Uruguayan dragged his touch too far wide, however, and the home defenders were able to clear the ball out for a throw-in.
At the other end, Suarez’s fellow South American Hulk made his own jinking run into the box but was expertly stopped by Jamie Carragher, before the Brazilian then struck the post from a tight angle after 27 minutes.
Suarez then got his third golden opportunity to give the visitors a precious away goal on 40 minutes, as Allen delivered a cross into the box that eventually worked its way to the 26-year-old.
But, amazingly, the Uruguayan’s back-heeled finish floated inches wide once again and both sides headed into the dugout soon after wondering how it was still goalless.
Straight after the restart, Glen Johnson was denied by Malafeev and Suarez fired wide from outside the box yet again.
But the Reds, whose chance conversion rate this season is a lowly 12%, were just too profligate to make a difference.
And on 70 minutes, they paid the price. Hulk stole possession inside the Liverpool half and sent a thunderous strike into the top corner, leaving Reina – who was otherwise sensational on the night – with absolutely no chance.
And Zenit then doubled their lead instantly as substitute Semak snuck in with a great run and got on the end of Aleksandr Anyukov’s cross to tap in at the far-post
The result leaves the Reds in real danger of elimination, and a tense second leg at Anfield now awaits.