The deposed Premier League champions came into Wednesday's game knowing that anything other than a victory might not have been enough for their top-four ambitions.
Jurgen Klopp made only one change to the side that saw off West Brom last weekend, with Gini Wijnaldum coming in for Curtis Jones in midfield. The hosts welcomed fans to Turf Moor for the first time in over a year.
A dominant first-half display saw Liverpool control proceedings. However, they were let down by poor finishing, with Thiago Alcantara, Mo Salah, Sadio Mane and Nathaniel Phillips all spurning very good chances.
Burnley sought to catch their opponents out on the counter and came close through Chris Wood and Dwight McNeil.
Just when it seemed like the sides would go into the break level, Roberto Firmino showed great composure and technique to score after being found by Andrew Robertson.
The second half started in the best way possible for Liverpool after Nat Phillips rose highest to head home Sadio Mane's cross into the box. Alex Oxlade-Chamberlain then stepped off the bench to make sure of the result with his first goal of the season.
The victory made it nine games unbeaten in the league for Liverpool, with their last four games ending in a win. Meanwhile, Burnley have now gone 10 home games without a victory in the Premier League.
Here are five talking points from the game.
#5 Liverpool take a giant step towards UEFA Champions League qualification
Leicester City's 2-1 loss to Chelsea on Tuesday opened up a world of opportunities for Liverpool to reclaim the initiative in the Premier League top-four race.
A victory for the Reds at Turf Moor would have put their fate in their hands for a top-four finish.
For most of the game, it looked like the Anfield outfit would pay the price for their profligacy in front of goal, but an improved second-half display saw them secure an important win.
With the win, Liverpool climbed into the top four for the first time since February and are now in control of their destiny.
The emphatic nature of the victory further boosts their cause, as they now hold a +4 goal difference ahead of Leicester City.
#4 Roberto Firmino continues fine run against Burnley
Roberto Firmino has played a key role in Liverpool's transformation over the last few years. However, the Brazil international has faced a lot of criticism for his low numbers in front of goal.
The 29-year-old came into Wednesday's encounter having scored just eight goals from 34 league games this season, and this is hardly impressive for a player leading Liverpool's line.
Despite his struggles in front of goal, Firmino's abilities are not in question, and he brought that to the fore with his well-taken opener against Burnley.
The goal means that the former Hoffenheim man has now scored in his last three games at Turf Moor while also bringing his record against the Clarets to five goals in nine games.