The Clarets climbed to sixth in the Premier League table as a result, taking their points tally to eight, with five of those accrued away at Chelsea, Tottenham and the Reds.
Nick Pope was all smiles in the tunnel at Anfield ahead of his first Premier League start, displaying minimal symptoms of apprehension, and an early touch from Daniel Sturridge's shot would've played a huge part in allaying any nerves.
Crystal Palace had 65% possession at Turf Moor last weekend, producing 23 shots on goal, and it was arguably the ideal conditions for the former Charlton Athletic striker to step in to following Tom Heaton's injury ahead of a trip to Merseyside.
The 25-year-old, who had made a vital save to deny Christian Benteke in the victory over the Eagles, was in for a busy day as the Reds celebrated their 125th anniversary but once again his team-mates helped limit any genuine threat.
Trent Alexander-Arnold, playing in an advanced position down the right hand side, had the next shot on goal, moving past Robbie Brady, working the ball on to his left boot before pulling his shot wide of the near post.
A coming together between Mohamed Salah and James Tarkowski inside the penalty area drew several half-hearted appeals for a spot kick which, according to replays, referee Roger East made the correct decision to ignore.
It was almost a training ground session for the home side at times as they confidently played the ball around the park but still they were unable to find the innovation to breach Burnley's defensive line.
Philippe Coutinho, making his first top flight start of the season following interest from Barcelona in the summer, tried his luck from 20 yards out but his effort took a nick off the boot of Steven Defour and looped over the crossbar.
And even on the rare occasion that the hosts did infiltrate, Salah wasn't in a position to threaten with the header as Sturridge supplied the cross beyond Stephen Ward.
There was no doubt that it had been Jurgen Klopp's side that had been making the moves but the Clarets are a different animal on the road this year and they always seem to have something up their sleeves.
With champions Chelsea and Spurs having already felt the wrath, Scott Arfield gave the visitors a surprise lead in the 27th minute.
Brady got the ball rolling when beating Joel Matip to Tarkowski's long ball, record signing Chris Wood got a toe end on the ball to create the opening and Arfield made no mistake, confidently passing the ball first time beyond Simon Mignolet.
Burnley's next challenge was to preserve that advantage against a side that scored frequently on their own turf. However, they held out for just three minutes.
Liverpool went route one on this occasion, with Emre Can able to pick his pass from deep, and once Egyptian international Salah held off Ward he fired the ball low past Pope.
The hosts put everything in to getting their noses in front before the interval but by hook or by crook the Clarets held out.
Sturridge was a whisker away from converting James Milner's cross after Tarkowski failed to cut the ball out and then the striker rifled the ball in to the side-netting after being fed in to the box by Coutinho.
In the closing stages of the half, after Salah had curled the ball in to the arms of Pope, Ben Mee went close to restoring the away side's lead when beating the offside trap to meet Brady's set-piece, getting beyond Roberto Firmino, but the defender couldn't find the target with his header.
Burnley were, to a man, brilliant after the break, once again putting everything on the line to keep their opponents out in a determined and disciplined display.
Liverpool were always going to create chances with a squad oozing with flair but the Clarets battled to claim a fifth point on the road.
Coutinho's wizardry opened up a path to the edge of the box early on but the one-time Inter Milan maestro drilled his effort over the crossbar.
Pope stood up to the task when denying both Can and Sturridge as the half wore on, with the latter a fabulous stop to his left hand side to beat the ball away.
The Clarets weren't without their chances, though, and Mee could've secured all three points on a couple of occasions in quick succession.
The centre-back was denied by Matip on the line when his header from Brady's corner had arched rainbow-like over Mignolet and from the resulting set-piece the Belgian stopper denied the former Manchester City academy product at his near post.
The hosts applied the pressure as the clocked ticked towards the 90 minute mark and pope did his confidence no harm when plunging to his left hand side to block Alexander-Arnold's volley from Milner's cross.
Liverpool did go incredibly close with the last attack of note when substitute Dominic Solanke, who had replaced Coutinho, guided the ball on to the bar from close range following good work from Alexander-Arnold.