Stewart Downing's second-half goal gave Liverpool a slender first-leg advantage against Belarusian side Gomel in their Europa League third-round qualifier.
The Reds rode their luck at times, and their only notable shot on target was when Downing cut in from the right and buried a shot past Vladimir Bushma.
The goal came just three minutes after Sergei Kozeka had rattled the post with a shot, and Dmitry Platonov fired the rebound wide from six yards.
Aleksandr Alumona also went close.
- Appearances: 700
- Goals: 5
- Debut: Jan 1997 v Middlesbrough
- Honours: Champions League 2005, Uefa Cup 2001, FA Cup 2001 & 2006, League Cup 2001, 2003, 2012
- England caps: 38
In his first competitive game as Liverpool manager, Brendan Rodgers handed a start to Joe Cole - only to see the midfielder, who spent last season on loan at Lille, limp off injured after just 23 minutes.
It was hardly an ideal start for the Premier League visitors, who struggled to assert their authority on their workmanlike hosts.
There were glimpses of the passing principles which earned Rodgers so much praise during his time as Swansea manager but, far too often, possession was squandered.
Jamie Carragher, making his 700th appearance for the club, had to be alert in the first half when he timed a block to perfection as Alumona shaped to shoot.
Sergey Matsveychyk also went close when he fired home from close range, with Liverpool failing to register a single shot on target in the first half.
They looked short on inspiration up front without Luis Suarez and Craig Bellamy, who are on Olympics duty, and Andy Carroll, who did not travel because of a slight groin strain.
New signing Fabio Borini toiled away, but it took some creativity and adventure from Downing to break the deadlock.
The winger cut in from the right and fired a left-footed shot into the bottom corner to give Liverpool a fantastic chance of progression in the second leg at Anfield next Thursday.
After the match, Rodgers was pleased with the result and performance - but asked for patience as he tries to assert his influence on the team.
"It will take time until Liverpool start playing the way Swansea did last season (tactically)," he said.
"Actually the way you play depends on the players you have.
"As for today I saw two things which were very important for me, I saw desire and commitment. I am very grateful to my players for a good game.
"This was my first competitive game in charge of Liverpool and for me it didn't really matter whether the game was played in Belarus or Brazil as I am really honoured to manage this side."
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