Striker David Ngog's goal nine minutes from time eventually broke the resistance of a determined Unirea Urziceni at Anfield in the Europa League.
With the visitors intent on soaking up plenty of pressure Rafael Benitez's side struggled to find the creativity to get past the massed Romanian ranks.
However, the Frenchman's close-range header meant the Reds have some breathing space as they head to Bucharest for next week's last-32 second leg.
The victory was only Liverpool's third in nine European fixtures since they hammered Real Madrid 4-0 in the last 16 of the Champions League 11 months ago - a disappointing run which contributed to their exit from Europe's elite-level competition in December.
Their job would have been easier had Steven Gerrard converted their first chance after just 25 seconds when Unirea lost possession straight from the kick-off.
Albert Riera and Dirk Kuyt linked up for the Dutchman to put the midfielder through but his side-foot shot was tipped over by goalkeeper Giedrius Arlauskis, who then punched away the Liverpool captain's corner.
Unirea's 4-5-1 formation meant they were happy to keep 10 men behind the ball and when Liverpool gained possession they all immediately retreated to the halfway line - meaning the hosts had to work hard for their openings.
However, Kuyt enjoyed some luck in the 10th minute when his heavy touch in the penalty area was not cleared and he followed up to flash a shot across goal which Arlauskis tipped past the post.
Gerrard was next to miss a chance, planting a 12-yard header from Riera's cross well wide.
Riera tried his luck from distance in the 26th minute but his left-foot drive was deflected wide by George Galamaz.
The game had taken on an attack versus defence training exercise with Unirea rarely venturing forward.
When they did, with a counter-attack just after the half-hour, Marius Onofras attempted an audacious lob over Jose Reina from the halfway line wide on the right but the Spain goalkeeper comfortably claimed.
Javier Mascherano's 30-yard drive was deflected wide by Razvan Paduretu while Ngog's shot on the turn from just inside the penalty area was also diverted wide.
Five minutes before half-time Bruno Fernandes was booked for bringing down Gerrard as he looked to burst clear but Daniel Agger drilled the 35-yard free-kick straight into the wall.
Heartened by their first half performance Unirea looked more inclined to go forward after the break but it was Liverpool who had the first chance with Gerrard heading wide again from Jamie Carragher's 52nd-minute cross.
Pablo Brandan was booked for tripping Gerrard in the centre-circle, ruling him out of next week's second leg through suspension.
Had Paduretu shown more composure on the edge of the area Liverpool could have been in trouble but the midfielder hacked wildly over.
Fabio Aurelio's low drive was on target but he was denied by a good low save from Arlauskis.
The ineffective Riera was replaced by Ryan Babel for the last 28 minutes and he began encouragingly with two decisive runs, the latter resulting in a cross to Gerrard at the far post which the England international could not keep in.
Mascherano was booked for a foul on Iulian Apostol as Liverpool continued to labour.
Martin Skrtel should have put the home side ahead in the 71st minute but he headed over Aurelio's inswinging corner from five yards.
Benitez sent on reserve team striker Daniel Pacheco, making only his second appearance in Europe, for Alberto Aquilani with quarter of an hour remaining.
Mascherano was caught in possession by Apostol, who charged forward 20 yards before curling a shot woefully wide.
With nine minutes to go the breakthrough finally came, with Pacheco playing an important part.
The diminutive Spaniard, possibly the smallest player on the pitch, out-jumped his marker at the far post to head back across goal for Ngog to nod in from five yards.
Gerrard fired just wide in the closing stages as Liverpool pushed for the second which would give them a cushion ahead of the second leg.Reuse content