Liverpool boss Jurgen Klopp was always confident Luis Diaz could have an impact at Luton Town.
Tahith Chong had Luton 1-0 ahead on 80 minutes and the hosts entered stoppage time still with the lead.
But substitute Diaz leapt highest to head home a Harvey Elliott cross to score on 95 minutes.
The winger then lifted up his shirt to show a t-shirt with the message 'freedom for papa', as he and his family wait on news of the release of his father by kidnappers.
Klopp said: "A wonderful moment but it doesn't change the situation. Most important thing is that his father gets released.
"It is wonderful he wanted to be here. That's it, for us a super important goal and for him very important and emotional, but that's it.
"He can always do that. When he is on the pitch he is always involved in special things.
"We knew he would be a threat, we didn't know how long he would play because he only had a few sessions with the team but that is not the most important part today. He scored the goal but we need to see some improvement in Colombia."
