Despite trailing in nearly every match stat, Sean Dyche's side held firm to continue its impressive start to the season.
The second half began in similar style and the Burnley goalkeeper was kept busy. James Tarkowski directed a long diagonal towards Robbie Brady, who got the better of Trent Alexander-Arnold in the air.
Liverpool were relatively untroubled for most of the game, but they always find a way to stumble in matches.
Liverpool welcome Burnley to Anfield in the Premier League on Saturday afternoon, and are big favourites to pick up all three points given the gulf in class between the two sides.
Jurgen Klopp's side have won just five out of 13 top-flight matches when Sadio Mane hasn't started.
With young 'keeper Nick Pope taking his place, the Clarets debutant looked nervous between the posts, but was rarely tested having only three shots on target to contend with.
Burnley man Jonathan Walters has previously netted on seven occasions against Liverpool.
Burnley has picked up away points at three of last season's top-six teams, beating Chelsea on the opening day and drawing against Tottenham at Wembley.
Ragnar Klavan gets into a clash in front of Liverpool's goal. One player came in for a lot of criticism for their failure to beat Burnley. "We didn't want to change him, it looked a little bit confused when we brought the subs on because I asked him and it was a thumbs-up".
"Result-wise, you are right, but honestly, as a person I'm not like this". We made seven changes but we were still really fluent, offensive football, dominant football. Burnley have played well so far this season, while Liverpool are a good team and deserve to be favourites they do not deserve to be favoured by 2 goals. But only one goal.
"When you have shots on goal it's not about their defending".
After Ben Mee had a header cleared off the line by Joel Matip late on, substitute Dominic Solanke hit the crossbar from just a few yards out as Liverpool - who were held in midweek by Sevilla in the Champions League - were frustrated again.
Liverpool manager Jurgen Klopp has praised Burnley boss Sean Dyche for the work he has done with the club - claiming that the way he has the Clarets organised makes it very hard to play against.