Stand-in captain Jordan Henderson led from the front with his second goal in successive matches as Liverpool maintained their pursuit of a top-four place.
With third-placed Arsenal and Manchester United also winning, Brendan Rodgers' side could not afford anything less than three points and a straightforward 2-0 victory over the Premier League strugglers was the achieved with the minimum of fuss.
Henderson, in possession of the armband in the absence of Steven Gerrard, back in training this week after a hamstring injury, slotted home just before the half-hour and Daniel Sturridge's header just after the break sealed the result.
With Henderson, and the team, in this form the watching captain - who departs for Los Angeles Galaxy in the summer - must be wondering where he fits in.
Liverpool, the league's only unbeaten side since the turn of the year, have not been defeated in the last 12 league games - picking up 30 points from a possible 36 having won seven of the last eight with six clean sheets.
Rodgers' side are upwardly mobile and moved back into fifth place, which they had been ousted from by Southampton 24 hours earlier, remaining three points behind Arsenal and two behind United, who visit Anfield a week on Sunday.
Burnley, on the other hand, have just one win in the last 12 league matches and stay second-bottom three points from safety.
Just 24 seconds had elapsed when Sturridge brought a smart reaction save out of Tom Heaton low to his left after Raheem Sterling had cut the ball back
But if the hosts thought that was the beginning of the onslaught they were mistaken as Burnley recovered their composure quickly and set out their stall to harass and make things difficult.
They achieved that with plenty of endeavour but despite gaining the upper hand in the game, what they lacked was that touch of class.
Liverpool have that in spades in the form of Philippe Coutinho, who pulls the strings in the space between opposition defences and midfield, and he was soon demanding and receiving more of the ball.
The clever brain and quick feet of the diminutive Brazil international have always been a characteristic of his play but what he has added to his game with devastating effect is shooting power.
Two wonder goals in successive matches have given the 22-year-old the confidence to have a go and when he let fly from distance the shot rebounded off a crowd of defenders to Henderson who, having also found the net in Sunday's win over Manchester City, rammed home from the edge of the area.
It was the first time in his senior career the 24-year-old had scored in consecutive matches.
Three minutes later Coutinho almost replicated his brilliant effort against City from a similar position but although he wrapped his right foot around the ball to impart plenty of spin the shot bent just around the far post.
It encapsulated the match as a whole. Liverpool, having spent £120million in the summer, had far more quality to call upon than Burnley, who make up for the difference in financial clout with committed players who carry out manager Sean Dyche's game plan effectively.
Goalkeeper Tom Heaton had to deny Sturridge three times in the first half alone: once from a direct shot, second time racing out to snatch the ball off striker's toes when Emre Can's deflected effort looped up off Michael Keane and then sticking out a leg to win a one-on-one with the England striker.
Burnley, for all their hard work and desire to go toe-to-toe with their opponents could not create half as much with Danny Ings, a reported target for Liverpool this summer, robbed by a perfect tackle from Martin Skrtel six yards out and Ashley Barnes heading at goalkeeper Simon Mignolet moments before the break.
Six minutes into the second half the Clarets were exposed again as Adam Lallana led the defence a merry dance with some nifty footwork to retain possession long enough for support to arrive in the form of Henderson, whose cross to the far post was nodded in by Sturridge.
Barnes volleyed wide to provide a reminder the Premier League strugglers were far from finished while Ings, as was the case for his team, came up just short in a race with Mignolet.
As a player myself who relies mainly on running around a lot in lieu of any real discernible talent, it feels fitting to be writing a piece highlighting the Premier League players who have covered the greatest distance this season.
Most of us would make terrible owners or CEOs of football teams. The reflex response from fans when their team is struggling is generally to sack the manager and keep the turnover going; at least it'll keep things interesting and hey, he can't be worse than the last guy.