The 18-year-old local lad retained his place in the squad after starting against Watford, continuing to deputise for the injured Nathaniel Clyne.
And he impressed as the Reds inflicted defeat on the German side at home for the first time since May 2016, breaking the deadlock midway through the first half with a stunning free-kick.
Having been assigned corner-taking duties during the 3-3 draw at Vicarage Road on Saturday, Alexander-Arnold stood over the set-piece alongside Alberto Moreno and Emre Can confidently.
Just a two-stride run-up was all he needed to whip the ball up and over the wall, nestling it into the bottom corner while keeper Oliver Baumann stood rooted to the spot.
The stunning set-piece left fans speechless after a clip of the goal was posted online.
“How about that for his first ever goal,” read one comment.
Another said: “He had a great game too, future is bright for that kid.
“It'll be great to have him for a couple of years before Barcelona come calling.”
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“He's showing amazing promise,” a third agreed.
“He is 100% the standout player on the pitch right now. Every time I see a great pass, interception, or run he's the culprit. And only 18, the sky is the limit as long as he doesn't lose his discipline and matures well.”
After the game, coach Jurgen Klopp praised his young prodigy for having the bravery to step up and take the free-kick.
“I have to say for an 18-year-old to have the balls to kick a free-kick like that is more interesting and exciting for me than a little mistake he made,” said Klopp.
“It was an intensive game for him. He has still some things to learn. He thought it [Hoffenheim goal] was offside but it was obviously not offside, unfortunately. Trent is a great player and I have to say I would rather have 2-1 than 1-0.”