Shortly after Mohamed Salah broke the deadlock midway through the second half, Alexander-Arnold stepped up to take control of a set-piece situation 25 yards from goal.
The No.66 produced an unstoppable shot, swerved over the Watford wall and into the top right corner to double a lead that was later added to by Roberto Firmino at Vicarage Road, as the Reds increased their unbeaten run in the league to 13 games.
Post-match, Alexander-Arnold explained how he came to be the man with the responsibility at the free-kick – and then use it in sublime fashion.
“Before the game, me, Hendo, Millie, everyone was joking about who would take it,” he told Liverpoolfc.com.
“I think Hendo wants one so he stepped up with the ball in his hand. Then he passed it to me because the gaffer said before the game that me and Shaq would be on them.
“So that’s why when you look back at it, me and Hendo had a little moment together when we celebrated as a bit of a joke.
“It’s always good to be able to score and contribute to a win; we were happy to get the win first and foremost.”
In his assessment of an encounter that was goalless after 45 minutes, Jürgen Klopp noted that Liverpool had to change their rhythm more often in the second half.
A ruthless display by the Reds followed and another clean sheet, too; never before has the club conceded as few as five goals at this stage of a league campaign.
“That’s just the confidence that we have got at the minute,” said Alexander-Arnold.
“We are not going to concede that many goals – and the forwards can score the goals. As long as we keep that belief then I’m sure we will keep getting these types of results.
“It was a tough game. It’s always tough when we come here.
“In the first half we found it quite tough but we managed to keep them out and we knew if we kept going we would get a good chance at goal ourselves. That came in the second half and the later it went on, the better it was for us to break them down.”
Watch: The key moments at Vicarage Road
Only Ian Rush has scored more goals for Liverpool against Watford than Salah, whose knack in meetings with the Hornets continued with a sixth strike in three appearances.
It was the Egyptian’s ninth in all competitions this term.
“He’s a world-class player and he shows that week in, week out,” added Alexander-Arnold.
“He has shown he can adapt to a different role and he has shown that with the goals he has scored so far this season. It’s not really fazed him.”