(Liverpool win 5-1 on aggregate)
Liverpool substitutes Steven Gerrard and Djibril Cisse struck late on as Liverpool cruised into the Champions League third qualifying round.
The holders were in lack-lustre mood after establishing a comfortable advantage from the first leg.
But Gerrard broke the deadlock with an angled drive after 77 minutes.
And Cisse scored from close range with five minutes left, with Liverpool's only worry a hamstring injury for £7m new boy Peter Crouch.
Liverpool boss Rafael Benitez rested eight players from the first leg in Lithuania, including Gerrard and Jamie Carragher.
He partnered Fernando Morientes and Crouch up front, with the signing from Southampton making his home debut.
But Crouch had little chance to make an impact in a tedious first 45 minutes, in which Liverpool enjoyed almost total domination of territory and possession but carved out few chances.
The clearest opportunity came after 14 minutes when Bolo Zenden's throw in missed out Crouch and Morientes saw his header saved by Sarunas Kilijonas.
Liverpool made a change at half-time, replacing the bitterly disappointing Morientes with Cisse.
Cisse instantly injected much-needed life into proceedings with a run and rising drive that was narrowly off target.
Kaunas were almost gifted an opportunity after 53 minutes when Sami Hyypia sent a clearance straight to Mukri Manchkhava, but he shot well over.
Liverpool suffered a disappointment just after when Crouch pulled up clutching his hamstring and was replaced by Darren Potter.
Hyypia almost made amends after 69 minutes when he thumped a header on to the bar from Didi Hamann's corner.
Gerrard was introduced after 74 minutes, and claimed Liverpool's opener three minutes later.
He fired in an angled drive which was fumbled in by keeper Kilijonas under pressure from Garcia, with Gerrard being credited with the goal.
That goal continued the Liverpool captain's record of having scored in every game so far during his side's defence of their Champions League crown.
Garcia set up the second for the lively Cisse with five minutes left, with a delightful cross that was expertly slotted home by the French striker.
Liverpool: Carson, Finnan, Hyypia, Whitbread, Warnock, Luis Garcia, Hamann (Gerrard 75), Sissoko, Zenden, Crouch (Potter 55), Morientes (Cisse 45).
Subs Not Used: Reina, Riise, Alonso, Carragher.
Goals: Gerrard 77, Cisse 86.
FBK Kaunas: Kilijonas, Kancelskis, Zelmikas, Baguzis, Manchkhava, Pehlic (Barevicius 66), Vadim Petrenko (Klimek 45), Kvaratskhelia, Kunevicius, Poderis (Maciulis 87), Rimkevicius. Subs Not Used: Kurskis, Beniusis, Kijanskas, Papeckys.
Ref: Gianluca Paparesta (Italy).