Diaz was back in the Liverpool squad following the kidnapping of his parents in Colombia at the end of October, and the 26-year-old came off the bench to head an equaliser for the Reds in the final exchanges.
Ex-Manchester United attacker Tahith Chong thought that he had scored the winner for Luton in their first-ever Premier League match with the Reds, but Diaz’s 95th-minute effort meant that the points were shared.
The result has moved Rob Edwards’s side out of the relegation zone and into 17th position in the table, while Liverpool remain fourth, boasting 24 points from their opening 11 matches.
Luton’s last clash with Liverpool ended in a 5-0 defeat in the FA Cup back in January 2008, but the promoted outfit more than matched the Merseyside side on Sunday.
Liverpool goalkeeper Alisson had to keep out a powerful drive from Ross Barkley in the fifth minute of the contest, before Thomas Kaminski made a smart stop to deny Darwin Nunez down the other end.
Nunez had another chance in the ninth minute of what was a lively match following smart work from Diogo Jota, but the Uruguay international could only fire his effort into the stands.
Trent Alexander-Arnold then released Nunez inside the Luton box in the 13th minute, but the striker fired wide, with the home side surviving another dangerous moment.
Luton’s first real chance arrived in the 15th minute, with the ball being worked to Issa Kabore at the far post, but his effort was always rising over the Liverpool crossbar.
Kaminski was again called into action to deny Nunez shortly after, before Mohammed Salah sent one over the crossbar in the 22nd minute after a dangerous Liverpool free kick into the Luton box.
Luton’s goalkeeper made another excellent stop in the 33rd minute to keep out Jota’s near-post effort, before Barkley sent another one whistling over down the other end five minutes before the interval.
Only two additional minutes were played at the end of the first period, and the two teams went in level, with Luton impressing in the opening 45 minutes against the Merseyside giants.
Luton continued to match Liverpool in the early stages of the second period, with the Reds finding it difficult to work their way through what was a strong defence on Sunday afternoon.
Alexander-Arnold sent a long-range effort over the home side’s goal in the 63rd minute, before Carlton Morris had a shot, which looked to be heading in, saved by Alisson two minutes later following excellent work from Chiedozie Ogbene in a wide area.
Cody Gakpo flicked one just wide of the Luton goal from a Harvey Elliott cross in the 69th minute, before Nunez somehow fired a Salah header over from a dangerous position, but the offside flag saved his blushes.
Kaminski made another excellent save to deny Nunez in the 72nd minute, with Liverpool looking dangerous in the final third of the field.
Luton made the breakthrough in the 80th minute of the match through Chong, who made the final contribution to a fast counter-attack, with the forward converting a low cross from Kabore.
There was a VAR check for a possible handball on Barkley inside the Luton box, but the goal was allowed to stand, with the home supporters able to celebrate the goal for a second time once the decision had been made.
Ibrahima Konate headed just wide of the Luton post in the 86th minute, but Liverpool managed to level the scores in the 95th minute through Diaz, who headed a cross from Elliott into the back of the net at the far post.
Diaz’s mother has been rescued from the kidnappers, but his father remains missing, and the forward removed his strip to show a shirt which asked for ‘freedom for my father’, with his contribution in extraordinary circumstances securing a point for the Reds.
Luton will return to action away to Manchester United on Saturday, while Liverpool will resume their Europa League campaign away to Toulouse on Thursday night, before hosting an in-form Brentford in the Premier League next Sunday.
