Zenit, despite being in the middle of their winter break, played extremely well and two goals in three second-half minutes by Hulk and Sergei Semak have left Brendan Rodgers' side with a mountain to climb if they are to reach the last 16 of the competition.
But it could have been very different for Liverpool if Luis Suarez had had his shooting boots on as the Uruguayan wasted four presentable goalscoring opportunities.
Last season's Russian champions started the match extremely brightly and, in the second minute, Pepe Reina did well to keep Aleksandr Kerzhakov's shot out.
When play swung to the other end, Suarez dragged his left-foot shot inches wide before Reina was forced to make another smart stop to deny Hulk.
When the match settled down, Zenit defender Nicolas Lombaerts allowed Suarez the opportunity to bear down on goal but the former Ajax striker over-ran the ball after he had rounded Vyacheslav Malafeev and the chance was lost.
Just past the half-hour mark, Reina was a little fortunate to keep Hulk's shot out. The Spanish goalkeeper parried the Brazilian's effort but the ball hit the post before eventually rolling away from danger.
Just before half time, Suarez wasted yet another good opportunity when he contrived to miss the target from five yards out after Joe Allen's cross had caused panic in the Zenit defence.
Early in the second half Glen Johnson rampaged forward and was allowed a shot that Malafeev was a little fortunate to parry away for a corner.
On the hour mark Suarez missed his fourth excellent chance, failing to find the target from the edge of the area after Stewart Downing had set him up.
Suarez's profligacy was to prove crucial as Hulk lashed an unstoppable left-footed thunderbolt past Reina before substitute Sergei Semak turned Kerzhakov's cross home from a tight angle to leave Zenit in the driving seat going into next week's second leg at Anfield.