The Clarets came flying out but found themselves behind just six minutes into proceedings when Darwin Nunez latched onto Cody Gakpo’s lay-off with a pinpoint first-time finish to end the striker’s 12-game goal drought.
Liverpool continued to carve out opportunities, with an instinctive Mohamed Salah effort being tipped over by James Trafford before Cody Gakpo sent a wild attempt off-target, but Burnley offered a reminder of their own intent when Josh Brownhill sent his strike curling agonisingly wide.
Liverpool went on to dominate the ball but Gakpo’s frustrations in front of goal continued as Trafford rushed out to deny the Dutchman, while a venomous strike was ruled out due to a Nunez foul on Charlie Taylor.
He still showed a creative spark with a ball through for Salah that resulted in the winger smashing a shot that struck the crossbar. Despite the pressure, Burnley kept their deficit to one goal going into the break as Trafford denied Wataru Endo and Salah.
Harvey Elliott thought he had marked his second league start of the season with a goal shortly after the restart but saw it ruled out after Salah was caught offside.
That moment roused the home supporters at Turf Moor and Jordan Beyer came close to raising the noise levels further when his attempt was deflected over by Nunez.
Sander Berge then dragged his shot wide before Jürgen Klopp showed his discontent with the game’s momentum by making a triple change in the 67th minute, although there was extra concern when Wilson Odobert created a glorious chance that Jóhann Berg Guðmundsson headed wide from.
After surviving a scare when Jacob Bruun Larsen fired marginally wide, Liverpool finally got their breathing space with Diogo Jota marking his return by sending his strike through James Trafford’s legs.
That helped Liverpool secure a third consecutive away league win to top the table ahead of Arsenal’s match against West Ham United on Thursday evening.
They also inflicted the 11th defeat from Burnley’s last 12 top-flight matches at Turf Moor, which keeps Vincent Kompany’s side five points adrift of 17th-placed Everton.
Flashscore Man of the Match: Virgil van Dijk (Liverpool)