Substitute Tahith Chong looked to have secured a sensational win for promoted Luton when he finished off a superb counterattack by slotting past Alisson 10 minutes from time.
Diaz entered in the 83rd minute and equalized in the fifth minute of added-on time, bundling in a finish off his shoulder from Harvey Elliott’s cross.
It was Diaz’s first appearance for his team since his parents were kidnapped in his native Colombia last weekend. His mother was rescued within hours by police but his father is still missing while negotiations take place.
Diaz lifted his Liverpool jersey to reveal a T-shirt with the words “Libertad Para Papa” (“Freedom for Papa”) after scoring.
On its first league visit in more than 30 years, Liverpool appeared rocked by a raucous atmosphere inside Kenilworth Road and was never at its free-flowing best against a side that dug in, ground out and waited for their chance.
Liverpool would have moved into second place in the standings with a win and is now third.
“I think we made it very difficult for ourselves,” Liverpool defender Virgil van Dijk said.
“It was always going to be difficult coming here, we have seen it with other teams coming here. You have to make it a bit easier for yourself and scoring a goal helps, it changes the dynamic of the game.”
Darwin Nunez had a slew of chances to score before Luton’s goal, with the Uruguay striker striking against the top of the crossbar from Trent Alexander-Arnold’s superb pass from deep in midfield in the first half.
He made perhaps the miss of the season in the second half, volleying horribly over from 2 meters (yards) out after Mohamed Salah misdirected a header on goal.
“Looking at the game, I think we didn’t deserve more than a point,” Liverpool manager Jurgen Klopp said. “We could have won the game with the chances we had but now looking at it I think we deserved a point.”