Dirk Kuyt headed an 85th-minute winner to snatch a 1-0 victory over Sparta Prague in Kenny Dalglish's first European tie as Liverpool manager.
Both sides had squandered numerous chances in a scrappy Europa League round of 32 encounter but Liverpool's superior quality was eventually rewarded by the hard-working Kuyt.
David Ngog, Joe Cole and Raul Meireles had also gone close in front of a sell-out 42,949 crowd which further underlined the gathering momentum of Dalglish's new regime.
Sparta, backed by 3,000 of their own raucous fans, contributed fully to an eventful, if low-quality, clash but were eventually undone as Kuyt profited from a late corner.
Liverpool captain Steven Gerrard, absent for the two previous games with a groin injury, was not risked and his dynamism and precision was missed throughout.
Christian Poulsen, whose partner had a baby earlier in the week, made little impact in a central role while Cole, starting for the first time under Dalglish, was quiet on the left.
The former Chelsea midfielder looked determined to kickstart his faltering Reds career, however, and broke clear early on to send over a looping cross which clipped the bar.
The opening stages were lively and suggested the game, which ultimately lacked quality, would be far more eventful than the drab first leg.
Liverpool appealed for a penalty in the second minute when a Meireles free-kick bounced and caught Manuel Pamic on the hand but nothing was given.
At the other end Libor Sionko headed over from a Kamil Vacek cross and a dipping shot from Vaclav Kadlec narrowly missed the target.
Both goalkeepers were tested by headers, Jose Reina first claiming a firm effort from Sinoko.
Sotirios Kyrgiakos then went close to handing Liverpool the lead when he rose to meet a Meireles corner but Jaromir Blazek saved well to his right.
Reina had a scare when he failed to claim a corner but Sionko was unable to take advantage and Meireles missed a good chance when he scooped a cross from the rampaging Martin Kelly over.
Blazek had an uncomfortable moment when he spilled a long-range shot from Cole, who had cut in from the left, but Liverpool could not capitalise.
Ngog tried his luck from distance as the ball dropped invitingly but miskicked as he turned to shoot.
Ngog had a better chance moments later as Kuyt cut inside to tee him up but the Frenchman chipped tamely at Blazek, who almost gifted a rebound opportunity to Cole but recovered.
Lucas also saw a 25-yard shot drift narrowly wide just before the interval.
Liverpool were forced to withdraw one of the first half's better players in Kelly at the start of the second period, but were able to replace the right-back with the experienced Jamie Carragher.
The hosts started brightly after the restart with Meireles volleying narrowly wide and then creating another attack with a superb long ball for Kuyt.
Kuyt raced on into the area and pulled back for Ngog but the lone striker again fluffed his shot.
Sparta also continued to threaten but Reina got down well to cut out a cross from Ondrej Kusnir.
Liverpool met more frustration as they tried to prise an opening with Kuyt having a shot blocked and Cole heading wide midway through the second half.
Liverpool pressed further with Meireles playing in Ngog but Blazek denied him.
Kyrgiakos was forced off for treatment after a clash of heads with Tomas Repka left him with a nasty cut above the eye.
He returned just as defensive partner Daniel Agger was forced off with injury and replaced by Martin Skrtel.
Kuyt, along with Meireles, had been one of Liverpool's most forthright players in the second half and his efforts were rewarded with his winner.
The Dutchman jumped above the defence five minutes from time to head firmly past Blazek and put the Reds into the last 16.
Cole should have added a second when he raced through on goal in injury time but sliced his shot wide.
Liverpool manager Kenny Dalglish felt victory was well deserved as his team
finally saw off Sparta Prague to reach the Europa League last 16.
Dalglish said: "I thought they made it really difficult for us tonight. In the first half there were a couple of scares and in the second half they had a header from a free-kick across goal. They were a good strong side and it was a difficult game for us across two legs but I thought we deserved to win.
"I think the boys deserve great credit for the way they went about their work - for their determination and their effort - to get a result. They were superb and the pride they took in themselves and the club was rewarded in the end with a goal.''
The Scot, who was appointed Anfield boss for a second time seven weeks ago, did
not lead the Reds into continental competition during his first spell due to the
ban imposed after Heysel.
The 50-year-old said: "I had never done it before and I quite enjoyed it. It's a fantastic football club and I was lucky enough to be asked to come back. But I'm only here managing a football club in the Europa League because of
the work that was done before me by the players and Roy.
"It is a great honour for me to be sitting here in charge of this football club but an even bigger honour to be here on a European night and also winning.''
Sparta coach Jozef Chovanec felt his team would have gonie through had they forced extra time.
The former Czech Republic national manager said: "It is very disappointing
because I was hoping we would get a chance in extra time. We tried to continue with our performance from last week, we tried hard
against the favourites for the game.
"Aside from the result we played very well but it is very disappointing to
concede a few minutes before the end. It was a goal from a corner. I didn't see that as a great goalscoring
opportunity and I think we could have shown more strength in extra time.
"Liverpool had injured players coming off and I am disappointed we didn't take
it to extra time.''