However, it was far from convincing and it needed a own goal by Remzi Kacar and a late strike from Dirk Kuyt to secure their passage.
Their one-goal advantage had been wiped out in the fourth minute when Teofilo Gutierrez side-footed past Jose Reina but the late double salvo ensured manager Roy Hodgson did not become the first Reds boss to exit Europe before the end of August.
The victory was Liverpool's first in Turkey against Turkish opposition and their hosts' first defeat at home in 2010.
Liverpool had chance to put the tie to bed in the first leg but taking a 1-0 lead to Turkey was never going to ensure a comfortable night.
And despite finding themselves under huge pressure in the opening 45 minutes they should have wrapped things up a lot sooner than they eventually did.
David Ngog missed two second-half chances which Fernando Torres, the man he was standing in for with the Spaniard resting back on Merseyside, would probably have buried.
Prior to that Sotirios Kyrgiakos - one of five changes from Monday's Manchester City defeat - could have scored in only the second minute but he directed a weak downward header from Fabio Aurelio's corner straight at Onur Kivrak.
Trabzonspor made no such mistake two minutes later when Kuyt gave the ball away and Gustavo Colman's intended shot sliced open the heart of Liverpool's defence and Gutierrez side-footed past Jose Reina.
The enthusiastic Trabzonspor support did not need encouragement to ratchet up the volume as Liverpool's task suddenly looked a whole lot more difficult.
A quick counter-attack from an Aurelio corner almost brought a second for Trabzonspor with Jamie Carragher deflecting Ibrahima Yattara's shot behind and then Colman drilling in a low effort which Reina turned around his left-hand post.
The Liverpool goalkeeper was receiving some unwanted attention from a fan with a laser pen and Croatian referee Ivan Bebek instructed the UEFA delegate to put out a warning that the game could be stopped as a result.
Hodgson's side struggled to gain a foothold in the game and spent the remainder of the first half under pressure.
That continued after the break as Burak Yilmaz burst through on goal three minutes after the restart but was flagged offside.
In the 52nd minute Ngog should have given Liverpool some much-needed breathing space when Cole stood up a cross to the far post but the Frenchman headed wide from close range when it seemed easier to score.
Ngog then turned his marker inside-out on the edge of the penalty area but, faced with a clear shot at goal, rolled his effort wide.
Liverpool were, however, growing in confidence as Trabzonspor began to drop deeper and deeper.
But the longer it went without a goal, the more pressure they put on themselves.
Hodgson made his first change with 13 minutes to go when he sent on Dani Pacheco for Aurelio.
But the breakthrough eventually came eight minutes from time when pressure by Ngog forced an own goal.
Johnson's run and cross down the right was turned in by Kacar via the near post.
And things were wrapped up late on as Kuyt tapped in after Kivrak could only parry out Pachecho's shot.
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