A questionable 20th minute penalty was awarded to the Potters when Jonathan Walters was brought down by Reds defender Jamie Carragher but there appeared to be minimal contact which prompted queries from the visiting side.
Nonetheless, the penalty stood and Walters hammered it down the middle against the run of play following a bright start by Kenny Dalglish's men.
An amazing second half saw Stoke keeper Asmir Begovic, aided by his defence, keep out about five Liverpool attempts which were produced by Jordan Henderson and Charlie Adam but they could not beat the determined Potters backline.
In injury-time, Luis Suarez called for a penalty for a handball from Matthew Upson but the Uruguayan was booked for protesting before he missed a golden opportunity moments later when he stabbed wide from straight in front which would have given his wasteful side a share of the points.
Liverpool finished the game having more than 70% of possession and over 20 attempts on goal to Stoke's three but were unable to find the back of the net as they come away with their first defeat of the season.
Yellow cards:STO - nil LIV - Luis Suarez 90+2'
Match facts:Liverpool have not won at Stoke since 1984.