Having been buoyed by Chelsea's earlier stalemate at Everton, Liverpool took full advantage of the Blues’ slip-up with a dominant display at Tottenham Hotspur Stadium, where Spurs did briefly offer hope of a fightback.
James Maddison pounced on a Mac Allister mistake to drag Spurs back into the contest, only for Dominik Szoboszlai to restore Liverpool's two-goal cushion on the stroke of half-time.
Mohamed Salah helped himself to a deserved double early in the second half, but Dejan Kulusevski's volley and Dominic Solanke's close-range prod made matters interesting.
Yet Liverpool's attacking prowess proved too much for Spurs to handle, and Diaz made sure of the points in the 85th minute, meaning Liverpool will top the tree at Christmas for the first time since the 2020-2021 season.
Salah took his tally of goals and assists for the season into double figures, becoming the first Premier League player to achieve the feat before Christmas, and first to do so in four successive campaigns.
"I didn't think about it before the game, but I'm glad I have done it, something that makes me proud. I'll keep working hard," he said.
"It's great to achieve [becoming Liverpool's fourth-leading scorer] at such a big club, but the most important thing is that we won the game. Wherever I am going to end my career, I am happy about it."
"Defensively, we need to improve as a team," he said. "Conceding three goals is quite hard. It’s a good result. Hopefully, we will just keep going.
"We expected that [a chaotic game], the way they play, they open the game, they enjoy their football, physically tough, and mentally we always have to be in the game.
"They don't change much in the way they play, it’s intense. [Manchester] City came here and struggled, other teams too. I'm happy we won because they play an intense game."
"It was a difficult day for us and a painful result. Credit to Liverpool, they are a very good side in a great moment. They are very settled and have great belief," Postecoglou said.
"It was a bridge too far for us. We were lacking a bit of energy and the ability to compete with them at the same level.
"I don't know how far we are from Liverpool. We are still growing as a team. We are 18 months into growing as a team," the Spurs boss said.
"We've had some challenges with the availability of players so it is hard to see where we are at. I'm really proud of the way the players played."
Asked whether the pressure is mounting on him, Postecoglou said: "I am not sure what you mean by pressure. I'm not happy with where we are. I think people are judging me, they're not throwing platitudes at me. That's fair enough.