Germany midfielder Emre Can's fourth goal of the season ended Burnley's stubborn resistance as Jurgen Klopp side Liverpool claimed an uncovering victory to strengthen their bid for a top-four finish.
Liverpool were far from their best and fell behind when striker Ashley Barnes turned home Matthew Lowton's emphatic defence-splitting pass.
The Reds equalised on the stroke of break-time with their first shot on target when Dutchman Georginio Wijnaldum poked in at the second attempt.
The former Bayer Leverkusen midfielder (Can) then secured a second-consecutive win for Liverpool with a long-range effort into the bottom corner.
The Sean Dyche side threatened to snatch an equaliser late on but Lowton hooked over from close range.
It was a match of few memorable moments but the victory means Liverpool, who remain fourth, are now five points clear of fifth-placed Gunners (Arsenal).
The visitors, who are yet to win a match away from home in any competition this season, are 12th.