An attempted cross by the right-back looped off Clarets striker Chris Wood and into the net in the first half at Turf Moor to give the visitors control of the contest.
Jürgen Klopp’s side used that momentum to rapidly double their lead through Sadio Mane, and Roberto Firmino sealed three points with a crisp drive late on.
The victory means this team’s active winning run in league football is the longest ever recorded in Liverpool’s history, surpassing the 12 set in 1990.
“We want to be setting records, we want to be doing good things. It’s always a good sign when you’re setting records for the club,” Alexander-Arnold told Sky Sports post-match.