The Merseyside giants came into the Anfield battle after Manchester City's 2-1 loss at the hands of Brighton & Hove Albion, giving Slot's men the chance to move five points clear of the champions at the top of the table.
Liverpool had to contend with early time-wasting tactics from Unai Emery's side, but they quickly broke the visitors' resistance, as Darwin Nunez finished off a blistering counter-attack after a Villa corner.
However, celebration turned to concern just a couple of minutes later, as Alexander-Arnold sat on the deck and eventually had to make way for Conor Bradley with an apparent injury.
The right-back briefly spoke with Slot before heading down the tunnel, and the Dutchman will no doubt be pressed for an update on the Englishman's condition in his post-game press conference.
Alexander-Arnold's early chance is also a concern for England boss Lee Carsley, who included him in his final Three Lions squad for this month's Nations League matches against Greece and the Republic of Ireland.
Liverpool - who are already without Alisson Becker, Diogo Jota, Federico Chiesa and Harvey Elliott - then return to action against Southampton on November 24, three days before a mammoth encounter against Real Madrid in the Champions League.