Luis Diaz came off the bench to salvage a point for Liverpool with a stoppage-time goal at Luton in his first match since his parents were kidnapped in Colombia.
Diaz's father remains missing, and the forward lifted his shirt to show a message of "freedom for papa" after heading in Harvey Elliott's cross five minutes into added time.
He later issued a statement calling for those holding his father to release him "immediately".
The 26-year-old former Porto player had last featured in a Liverpool squad 10 days ago, but manager Jurgen Klopp said before this match that Diaz "wanted to be part of the team".
His goal was a poignant and remarkable conclusion to a contest in which Luton had appeared on course for a deserved first league win of the season at Kenilworth Road and a first victory over the Reds since 1991.
Substitute Tahith Chong sparked wild celebrations among the home fans, who were eyeing a famous result after he steered in Issa Kabore's cross at the climax of a superb counter-attack with 10 minutes of the regulation 90 remaining.
Until Diaz denied Luton the win, Rob Edwards' well organised and athletic side frustrated Liverpool, for whom Darwin Nunez had a day to forget in front of goal.
The Uruguay forward went closest to breaking the deadlock with a dipping first-half shot that clipped the Hatters' crossbar. He was unable to convert several other opportunities and glaringly blazed over after Mohamed Salah nodded the ball to him in the six-yard box.
The result leaves Klopp's side third in the table, three points behind leaders Manchester City, while Luton have climbed out of the bottom three to 17th due to their superior goal difference over Bournemouth.
Luton put Liverpool off their stride
Liverpool arrived in Bedfordshire searching for their fifth consecutive win in all competitions, but only Diaz's late intervention spared them an embarrassing defeat against their unfancied opponents.
While Liverpool's summer outlay on players was around £150m, Luton spent in the region of £20m reinforcing their squad after completing a lengthy journey back to the English top flight.
Relegated from the First Division the season before the Premier League was founded in 1992, they went on to spend five years as a non-league club.
However, there was little to choose between the sides at times, with Luton's greater endeavour nullifying their opponents' obvious quality on the ball.
The Reds enjoyed plenty of possession and had 24 shots, but only six were on target and they appeared short of inspiration and efficiency in the final third until Elliott was introduced.
Had Diogo Jota stroked in an early chance it may have altered the complexion of the match, but he saw his hurried effort saved at the near post by Thomas Kaminski.
Only three of Nunez's nine efforts were on target, while Cody Gakpo flicked wide from another Elliott delivery from the right.
Klopp will also be concerned by the way Luton carved out openings, with Trent Alexander-Arnold struggling to contain Republic of Ireland winger Chiedozie Ogbene.
Ogbene surged past the England full-back during the first half to tee up Kabore and ghosted away from him and Ibrahima Konate in the second period to cut the ball back to Carlton Morris, who was denied by the onrushing Alisson.
The Brazilian keeper was unable to prevent Chong from finishing a move that started with a Liverpool corner, but Diaz was on hand to salvage a point for the Reds despite the ordeal he and his family are going through.
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