The hosts broke the deadlock shortly before the half-hour mark when Jordan Henderson lashed home a loose ball from 20 yards.
The stand-in skipper then turned provider for the second six minutes after the interval as his cross was nodded home by Daniel Sturridge.
Here, Sports Mole looks at whether Liverpool were worthy of all three points on Merseyside.
On target: 8
On target: 1
Was the result fair?
Absolutely. Liverpool were in control of this match from start to finish today, almost breaking the deadlock inside 30 seconds and going on to carve out a number of other chances before Henderson finally found the breakthrough. The hosts could have had this match wrapped up by half time but for some good goalkeeping from Tom Heaton and one or two instances of wasteful finishing.
In contrast, Burnley barely threatened at all in an attacking sense and never once really looked like scoring throughout the 90 minutes. Their one shot on target is an indicator of how little danger they posed to Simon Mignolet's goal, with Liverpool always looking comfortable in defence. There is no question that the Reds deserved to win this match, and in truth it could have easily been more than a two-goal margin between the sides.
Having taken 13 points from a possible 15 in matches against West Ham United, Everton, Tottenham Hotspur, Southampton and Manchester City in their five outings prior to this one, perhaps the biggest task for Liverpool tonight was to avoid complacency creeping into their game. Burnley provided the easiest opposition on paper that Liverpool had faced for some time, but they went about their job in a professional manner from the first minute to the last.
They played with the tempo and energy that has accompanied their recent fine form, showing no signs of fatigue despite a packed fixture schedule in recent weeks. The likes of Sturridge, Philippe Coutinho and Adam Lallana posed a constant threat to the Burnley defence, while at the other end of the field they comfortably coped with Burnley's attackers. Liverpool were superior in pretty much every area of the field this evening and that resulted in a routine win for the team.
The main downside to the performance was that they didn't win by more goals, but that will only be a minor concern for Brendan Rodgers. The win made it four in a row in the league and 12 without defeat as they march on towards the Champions League places. Today's performance wasn't quite as attention-grabbing as their display against Manchester City at the weekend, but it was no less important as they continue to build momentum.
Not many Burnley fans would have made the trip to Anfield expecting much, with their side struggling, particularly on the road, and Liverpool the form team in the division. Draws away to Manchester City and Chelsea earlier in the campaign may have raised optimism, but that was quickly dashed as Liverpool came flying out of the blocks, almost taking the lead inside the opening 30 seconds. Burnley did eventually settle into the first half, but almost all of their energy was spent on containing the hosts.
That is not to say the Clarets parked the bus, though. Sean Dyche had his side committing men forward whenever possible and their first thought was usually to get onto the front foot. However, that was very rarely an option as Liverpool dealt with their attacking threat with ease. The visitors sorely lacked a cutting edge in the final third and probably could have played until midnight without finding the back of the net today. Simply put, Burnley were just outclassed in this match, coming out second best in almost every department.
They worked hard throughout and didn't let their heads drop, but they lacked the quality to really make much of a game of it. The main worry for Burnley now is that they remain three points from safety with a horrendous run of fixtures to come. They face Man City, Southampton, Spurs and Arsenal in their next four games, meaning that they would have played eight of the current top nine in consecutive matches by the end of that run. They will do very well to still be in touch with those above them after that.
Sports Mole's man of the match
Jordan Henderson: With Steven Gerrard's impending exit edging closer and closer, Henderson has really begun to step up to the plate in recent weeks. He was instrumental again today, and perhaps the biggest compliment that could be paid to him was that his performance bore many hallmarks of Gerrard at his peak. His finish was a very good one from the edge of the box, while he also claimed a fine assist for the second goal. His long passing was impressive throughout the match too as he dominated the midfield area.
There weren't any major mistakes in this match, so we're going to pick on Sturridge for his miss shortly before half time. The striker was played through on goal by Coutinho and only had the keeper to beat, but Heaton made the stop. Credit must go to the Burnley man, but Sturridge will feel that he should have scored.
Lee Mason won't have had many easier matches to officiate than this one. The solitary yellow card didn't come until the 85th minute and there were no major decisions for him to make.
Liverpool: Liverpool turn their attention to the FA Cup on Sunday as they host Blackburn Rovers in the quarter-finals.
Burnley: It doesn't get any easier for Burnley as they welcome champions Manchester City to Turf Moor on March 14.