Ashley Barnes grabbed the winner from the penalty spot.
An Ashley Barnes penalty put an end to Liverpool's near four-year unbeaten home record in the Premier League.
Burnley came away from Anfield with a 1-nil victory last night to move seven points clear of the relegation zone.
Liverpool have now gone four top flight games without a goal, and five without a win.
The champions are six-points adrift of leaders Manchester United at the midway point of the season.
Manager Jurgen Klopp says the Reds can't be brilliant all the time.