The reds traveled to Kenilworth Road for the Sunday 4:30pm kick off.
After Arsenal's defeat yesterday, and with Spurs not facing Chelsea until tomorrow evening - the reds know that a win will propel them back into 2nd place, one point behind Man City at the top of the Premier League table.
This is Liverpool's first meeting with Luton for almost 16 years, and it is 31 years since they last faced them in the League - Luton relegated in what was the final season of the First Division - before the advent of the Premier League years.
Here's how the game unfolded.
As it happened...
Team news incoming.
Lots of changes, obviously, from the midweek League Cup game.
Luis Diaz is on the Liverpool bench today.
Alisson, Alexander-Arnold, Konate, Van Dijk, Gomez, Mac Allister, Szoboszlai, Gravenberch, Jota, Salah, Nunez.
Subs: Kelleher, Endo, Diaz, Gakpo, Elliott, Tsimikas, Matip, Doak, Quansah.
Certainly a lot of Premier League experience in the Luton Town midfield with Andros Townsend, Ross Barkley and Marvelous Nakamba all in the centre.
Kaminski, Osho, Lockyer, Mengi, Barkley, Nakamba, Townsend, Kaboré, Doughty, Morris, Ogbene
Subs: Krul, Giles, Mpanzu, Luker, Nelson, Chong, Clark, Brown, Adebayo
Teams are out on the pitch at this relatively small Premier League stadium.
Gomez making his first start at left back for 8 years, according to Sky Sports.
After a period of remembrance, including The Last Post, we are underway at Kenilworth Road.
4' Confident start from the reds, although a rare moment for Luton as Barkley drills a low shot at Alisson.
Nunez at the other end attempts another goal like the one he scored midweek. This one is pushed out for a corner.
13' Lovely ball forward from Trent. Nunez collects it on his knee at the edge of the area then smashes a right footed shot that hits the crossbar.
Great control from the Uruguayan.
16' Nunez with another curling shot from outside the area - keeper tips it away.
22' Free kick from Liverpool and the ball falls to the onrushing Salah, just in the area, who fires over the crossbar.
That was a great chance and probably should have resulted in a goal.
24' Cross comes in - it's a bit of stretch for Nunez but he does get his head on but it's not a clean connection - over.
31' No killer blow from Liverpool yet. You do feel if they get one then Luton will have to come out and attack in more numbers which could open the door.
At the moment though they are defending well.
32' Big chance for Jota who turns and fires at goal. He puts it the nearside though and he probably wanted to angle his shot into the far corner.
Keeper gets to make a save. Liverpool maintaining the pressure with corners though.
First half added time. Just the two minutes of it.
It remains 0-0.
Marvelous Nakamba booked just before half time.
Liverpool on top in terms of possession, shots and even expected goals. But the goals tally remains blank.
Salah with probably the biggest chance of the half, but Nunez was busy.
We are back underway. No changes from either side.
49' Plenty of fireworks lighting up the sky around Luton's ground (it is November 5th in the UK after all) but none on the pitch so far.
Szoboszlai urging Liverpool's centre backs to push up and bring the ball forward.
54' Alexis Mac Allister collects a yellow card. That's his 5th of the season and will mean he suffers a second suspension of the season - he will miss the game against Brentford.
56' Dangerous cross whipped in and Alisson had to be alert to collect that one.
The longer this 0-0 goes on, the more Luton will fancy their chances of nicking one.
A little bit of nervous tension beginning to creep in to Liverpool's play.
68' Triple change of Elliott, Gakpo and Tsimikas. Replacing Szoboszlai, Jota and Gomez.
70' Nunez and Gakpo with some gilt edged chances there to open the scoring.
Not quite sure how Liverpool aren't ahead in this game.
75' Yellow card for Jurgen. He greets the decision with a smirk.
15 minutes remaining for Liverpool to get a goal.
79' Gravenberch with another attempt that the keeper stops. Liverpool moving past 20 shots now in this game.
80' From a Liverpool move, Luton move on the counter quickly. And they put the ball in the back of the net. Chong with the goal.
Liverpool just done by the quick break that Luton executed well.
1-0 Luton. Total sucker punch.
83' Gravenberch replaced by Luis Diaz.
90+5' LUIS DIAZ HEADS IN THE EQUALISER!
'Libertadao pero papa' reads the message on Luis Diaz's shirt that he lifts up.
A minute left for a winner here at Kenilworth Road.
FT: Luton 1-1 Liverpool
Luis Diaz's goal salvages a point for Liverpool but that was definitely two points dropped by the reds.
You get the feeling a couple of years ago, in title winning form, the reds would have got an even later winner there.
On to the next game.
Liverpool lose a bit of ground to Man City at the top.