Liverpool reached the Champions League group stages after nervously edging past Israeli side Maccabi Haifa.
Crouch's goal owed much to the work of Jermaine Pennant
Striker Peter Crouch put Liverpool ahead early in the second half when he headed home Jermaine Pennant's cross.
But Roberto Colautti quickly revived Haifa's hopes in Kiev when he tapped home after goalkeeper Jose Reina was unable to hold Xavier Anderson's shot.
Late on Reina prevented Haifa from going ahead when he flung himself to his left to tip away Colautti's shot.
Liverpool's starting line-up was notable for the absence of Steven Gerrard, who was named as a substitute after suffering a stomach upset on Monday.
Gerrard eventually came on midway through the second-half after Mohamed Sissoko fell awkwardly.
Sissoko was not the only Liverpool player to go off injured with left-back Stephen Warnock having to be substituted early in the first-half to be replaced by Fabio Aurelio.
Haifa goalkeeper Nir Davidovitch kept his side in the game in the first half, making three superb saves to frustrate Luis Garcia.
Twice he made fine reaction saves from Garcia shots, but Davidovitch's most impressive stop came when he flung himself at a header from the Spanish international to clear the ball after a Liverpool corner.
Garcia's Spanish compatriot Xabi Alonso also went close with a curling shot that went narrowly wide.
With Liverpool dominating possession, Haifa found it difficult to create chances in those opening 45 minutes, though Yanov Katan did get the ball in the net, only for the goal to be ruled out for offside.
Early in the second half Alonso flighted a free-kick over the Haifa wall, an effort that gave Davidovitch an anxious moment before the ball curled wide of the post.
Soon afterwards Crouch put Liverpool ahead with that headed goal.
It was a goal that owed much to the initiative of Pennant, who skipped his way past Haim Magralishvili before picking out Crouch, who had made a darting run to the near-post.
Crouch's header gave Liverpool a 3-1 aggregate lead but it did not take long for Haifa to regain a foothold in the game.
Anderson burst into the Liverpool box before producing a shot that Reina was unable to hold, allowing Colautti to put the ball into the unguarded net.
Colautti's goal instilled a more adventurous approach from Haifa and Alain Masudi's volley and Gustavo Boccoli's strong run gave Liverpool a couple more unsettling moments.
With nine minutes to go Reina made a superb one-handed stop to tip away Colautti's dipping effort to ensure Liverpool will be in Thursday's Champions League draw.
Uefa had moved the game to Kiev due to the Middle East conflict.
Liverpool now go through to Thursday's draw for the group stages. The draw can be followed live on this website.
Maccabi Haifa: Davidovitch, Harazi, Magralishvili, Olarra, Keinan (Meshumar 65), Anderson (Melikson 71), Xavier, Boccoli, Masudi (Arbaitman 80), Colautti, Katan.
Subs Not Used: Al Madon, Kanan, Swan, Gazal.
Booked: Keinan, Anderson, Meshumar.
Goals: Colautti 63.
Liverpool: Reina, Finnan, Hyypia, Agger, Warnock (Aurelio 28), Gonzalez, Alonso, Sissoko (Gerrard 67), Pennant (Bellamy 86), Luis Garcia, Crouch.
Subs Not Used: Dudek, Kromkamp, Fowler, Zenden.
Booked: Alonso, Hyypia.
Goals: Crouch 54.
Ref: Roberto Rosetti (Italy).