Mohamed Salah spurned a glorious early chance to net his 44th goal of the season and Danny Ings saw a goal ruled out for offside before half-time.
Nevertheless, for all Jurgen Klopp's pre-match insistence upon the importance of their weekend engagement, it was a fitful showing from Liverpool, who will look to press home a 5-2 advantage over Roma in the Italian capital on Wednesday.
Stoke boss Paul Lambert continued his proud record of having never lost at Anfield in six visits and the well-drilled away team never looked likely to endure the sort of ordeal on the road that has seen them concede seven at Manchester City and five apiece to Tottenham and Chelsea this season.
Nevertheless, anything over than victories over fellow strugglers Crystal Palace and Swansea is unlikely to save Stoke, who almost found an 88th-minute winner heavily against the run of play through captain Ryan Shawcross. At this stage, even that might not be enough.
Anfield waited for the net to bulge in the fifth minute, but the only sight more surprising than Erik Pieters darting out of his defensive line to give Salah the freedom of Stoke's half was the PFA Players' Player of the Year dinking a routine finish wide.
Joe Gomez, one of five alterations to the XI that thumped Roma, made a shaky start and in the 20th minute his aimless lunge on Moritz Bauer allowed the Austria international to cross for Mame Biram Diouf to head wide at the far post.
Gomez was playing at right-back as Trent Alexander-Arnold pushed into midfield to fill the void left by Alex Oxlade-Chamberlain's knee ligament injury and the latter youngster should have done better when he prodded Salah's pass at Stoke goalkeeper Jack Butland.
There were chances at both ends as ex-Liverpool man Peter Crouch just failed to get on the end of Xherdan Shaqiri's low centre, while Georginio Wijnaldum rippled the side-netting and Salah did likewise from a 34th-minute free-kick.
Ings thought he had given Liverpool the lead four minutes before half-time but strayed offside before rifling Wijnaldum's return pass into the roof of the net.
A groin injury to centre-back Bruno Martins Indi came as a major blow to Stoke and Lambert's decision to send on winger Ramadan Sobhi underlined the Potters being in a situation where a 12th draw of the campaign would be of little use.
Stoke's Egypt international enjoyed a couple of forays, drawing a brave block from Gomez, but the visitors had faded as an attacking force.
Liverpool's hoarding of possession was the main factor that made a home breakthrough more likely in a half that ambled past the midway point as Alberto Moreno drove wide from 25 yards.
There was late drama as Pieters fortuitously survived a penalty shout for handball before Shawcross, a Stoke mainstay since their promotion a decade ago, came agonisingly close to smuggling home the winning goal his club badly needed.
Key Opta stats:
- Liverpool failed to score at Anfield in the league for the first time in nine games (since a 0-0 versus West Brom in December), after scoring 27 in total in the eight before that.
- Stoke City are without a win in 12 Premier League games, their longest run without a victory in the top flight since December 1984 (17).
- It's also the current longest winless run across the top four divisions of English football.
- The Reds mustered 20 shots without finding the back of the net, their biggest haul without scoring at Anfield in the league since April 2014 (26 v Chelsea).
- The Potters are without a win in 13 away league games (D6 L7), since a 1-0 win against Watford in October.
- Paul Lambert has taken charge of more Premier League games at Anfield without ever losing than any other manager in the competition (5 - W2 D3).
- Mohamed Salah mustered seven shots in the game (none on target), the most he has had without scoring in a single game for Liverpool in all competitions.