The games continue to come thick and fast for Liverpool, with this encounter coming during a spell of 11 games in 42 days.
At this point of the campaign, each clash is as important as the last, too - a victory here would have seen the Reds move four points clear at the top of the table, albeit having played a game more than second-placed Manchester City.
Against relegation candidates Luton, they could have been two goals ahead in the opening five minutes, but Luis Diaz first failed to get Caoimhin Kelleher’s long ball out of his feet after being played through on goal before curling another effort wide.
Jurgen Klopp was without all three of this season’s top goalscorers, with Mohamed Salah, Darwin Nunez and Diogo Jota all out injured.
As such, the hosts lacked cutting edge in front of goal - Diaz was the main culprit before the break, firing off a plethora of shots without really testing Marcin Kaminski between the Luton sticks.
Ultimately, the Hatters showed their opponents how it was done, as Chiedozie Ogbene headed into an empty net at the back post after Kelleher had directed Tahith Chong’s low shot into his path to give his side a surprise lead.
After the restart, it was initially more of the same as Liverpool struggled to trouble Kaminski.
However, in the space of an electric couple of minutes, the 19-time English champions turned the game on its head before the hour mark.
It started when a Cody Gakpo effort was tipped around the post, with Virgil van Dijk powering a bullet header into the back of the net from Alexis Mac Allister’s resulting corner.
Connor Bradley then saw a low attempt kept out by Kaminski’s leg before another Mac Allister pass found Gakpo in the six-yard box, allowing the Netherlands international to nod beyond the Luton shot-stopper.
Liverpool were firmly on top after the quickfire double and increased their advantage midway through the half.
Finally, Diaz had his goal, firing into the net with aplomb after being played in by Andrew Robertson.
In the final minute of normal time, Harvey Elliott caressed a shot into the top corner to add extra gloss to the win.
With 12 matches remaining, the hosts are in pole position to secure the title and send Klopp out on a high. Rob Edwards’ Luton, on the other hand, are still in the bottom three and, although there are plenty of positives to take from the game even in defeat, we are approaching the part of the season where results and points matter above all else.
Flashscore Man of the Match: Alexis Mac Allister (Liverpool)
