The Reds were handed a boost prior to Saturday's clash, Jordan Henderson returning to Premier League action for the first time since February and Andy Robertson named on the bench following an ankle injury.
It was Robertson's replacement, Konstantinos Tsimikas, who created the opener, finding Jota with a cross as the forward headed in his second goal in as many games at the start of the new season.
Both teams had strikes ruled out for offside, Mohamed Salah and Ashley Barnes the unfortunate pair, before Sadio Mane profited from Trent Alexander-Arnold's curling pass to seal victory.
Burnley had started the brighter, offering the hosts a rude awakening with Alexander-Arnold forced into a goal-line clearance to block Dwight McNeil's low effort - the offside flag belatedly appearing after the initial scare.
The hosts then opened the scoring in the 18th minute when Jota flicked past Nick Pope to record his first league goal at Anfield since November 2020.
Salah managed to curl past the Burnley goalkeeper to seemingly add a second, only for VAR to rule the Egypt forward offside after a smart offload from Harvey Elliott, making his first Premier League start for Liverpool.
James Tarkowski almost levelled on the stroke of half-time, rising above Alisson but heading narrowly wide as the goalkeeper failed to grasp Matthew Lowton's deep set-piece delivery.
Burnley had a goal of their own disallowed after the break, Barnes whipping into the roof of the net before seeing the assistant correctly raise his flag.
Any concerns among the returning home crowd over the slender lead were extinguished when Mane made Liverpool's second-half domination tell, smashing a low attempt into the net to cap superb build-up play by the hosts.
Alisson ensured a clean sheet with a brave save deep into added time, rushing out to deny Barnes from close range after the forward was rolled through by substitute Jay Rodriguez.